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REVIEW TEST 1

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- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

A. - 4

B. 4

D. - 1/2

C. 1/2

E. None of the above

Sorry, that answer is incorrect.

Remember slope is defined by

Where x1 and y1 are the coordinates of the first point.

Please try again.

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Great, the correct answer is 4, since -

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A. 3

B. - 3

D. 2/3

C. -3/2

E. None of the above

Not quite, that answer is incorrect.

Remember to find the slope you solve the equation for y and the slope is the coefficient of the x term –

y = mx + b

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Hey great, the correct answer is - 3/2, since

y = - 3/2 x + 9

And the coefficient of x is the slope.

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A. 6

B. 18

D. 9

C. - 6

E. None of the above

Too bad, that answer is incorrect.

Remember to find the y-intercept you solve the equation for y and the y-intercept is the b term –

y = mx + b

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OK, the correct answer is since 9 since

y = - 3/2 x + 9

And the constant term is 9.

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A. x 7

B. x > 7

D. x 7

C. x ≠ 7

E. None of the above

Not quite, that answer is incorrect.

Remember you may not take the square roots of negative numbers. Hence the interior of the square root sign must be positive. Solve for x in

x – 7 ≥ 0

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Terrrrriffffic, the correct answer is x 7,

Since x – 7 ≥ 0 means

x 7

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A. x ≠ 4

B. x > 4

D. x < 4

C. x ≠ - 4

E. None of the above

That answer is incorrect. It is a hard one!

Remember you may have a zero in the denominator. Hence x – 4 ≠ 0.

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Terrrrriffffic, the correct answer is x ≠ 4 ,

since the denominator may not be 0 and it is when x = 4.

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A. x = 0 and x = 2

- x = - 0.41 & x = 2.41

C. x = 0.41 and x = – 2.41

D. x = - 2 & x = 1

E. None of the above

Sorry that answer is incorrect.

There are at least three ways to find the x-intercepts:

1. Factor the quadratic and solve the two factors. (This one does not factor easily.)

2. Use the quadratic formula.

3. Graph it on our calculator and use ZERO under the CALC menu.

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Yes, the correct answers are –2.41 and 0.41.

I used my calculator and ZERO under the CALC menu.

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A. y = 0

- y = 0.41

C. y = – 2.41

D. y = - 1

E. None of the above

Too bad that answer is incorrect.

There are at least three ways to find the y-intercepts:

1. Let x = 0 and solve for y.

2. Use the fact that the y-intercept = c in the original equation.

3. Graph it on your calculator and use VALUE under the CALC menu with x = 0.

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OK, the correct answer y = - 1.

I used the fact that C = - 1 in the original equation.

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A. x = - 1 and y = - 2

- x = - 1 & y = 2

C. x = - 2 and y = – 1

D. x = - 2 & y = 1

E. None of the above

No that answer is incorrect.

To find the vertex:

1. Use the formulas:

2. Graph it on our calculator and use MINIMUM under the CALC menu.

OR

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Correctamundo, the answer is (- 1, - 2).

I used my calculator and MINIMUM under the CALC menu.

NOTE: You will need this answer for the next question.

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A. A maximum of - 2

- A maximum of 1.

C. A minimum of – 2.

D. A minimum of 1.

E. None of the above

No that answer is incorrect.

To find the maximum or minimum use the results of the previous question.

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Yes, the answer is a minimum of - 2.

See the results of the previous question #13.

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A. (x + h) 2 – 5 (x + h) + 3

B. x 2 + h 2 – 5x + 5h + 3

C. x 2 + 2xh + h 2 – 5x – 5h + 3

D. 3

E. None of the above

That answer is incorrect. It is a hard one! You must substitute correctly.

Remember that f (x + h) means that you are to substitute an x + h everywhere an x appears in the equation. In this problem substitute an x + h for x into x 2 – 5x + 3.

Don’t forget to simplify

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That answer is correct but you forgot to simplify!

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Grrrrreat, the correct answer is

x 2 + 2xh + h 2 – 5x – 5h + 3,

since (x + h) 2 - (5) (x + h) + 3 =

x 2 + 2xh + h 2 – 5x – 5h + 3.

NOTE: You will need this answer for the next question.

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A. x 2 + h 2 – 5x – 5h + 3

- 2x + h – 5

D. 2xh + h 2 – 5h

C. 3

E. None of the above

That answer is incorrect. It is a hard one! This is an important question.

Remember that the difference quotion is,

i.e. you need to divide the answer for question 11 by h.

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That answer is incorrect. It is a hard one! This is an important question.

Remember that the difference function is,

You forgot to do the final step and divide the difference by h.

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WOW, the correct answer is indeed 2x + h – 5.

NOTE: You will need this answer for the next question.

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A. m = - 2

- m = - 1

D. m = 1

C. m = 3

E. None of the above

Sorry that answer is incorrect.

Remember to find the slope of the secant you can do either of the following:

1. Work out the y values of the two points given and use the slope formula

OR2. Substitute x = 0 and h = 3 into the result of question 12.

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Great, Substitute x = 0 and h = 3 into

2x + h – 5

yields 0 + 3 – 5 = - 2

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A. y = x + 1

B. y = - 2x - 1

C. y = - x - 1

D. y = - 2x + 1

E. None of the above

No that answer is incorrect.

Use your calculator and the DRAW menu using TANGENT.

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Yes Yes Yes, the correct answer is y = - x – 1.

I used my calculator and the DRAW menu using TANGENT.

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A. 2

- 3

C. 1

D. - 1

E. None of the above

Sorry that answer is incorrect.

Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will work. Try it.

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Yes, the correct answer is 1.

Substituting 1 for x yields

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A. 1

- - 1

C. Undefined

D. 0

E. None of the above

Too bad that answer is incorrect.

Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will work. Try it.

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OK, the correct answer is 0.

Substituting 2 for x yields

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A. 3

- Undefined

C. 0

D. 1

E. None of the above

No, that answer is incorrect.

Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will not work since you get 0/0 for your answer. You must factor the numerator and denominator and cancel common factors before you substitute 3 for x.

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Correctamundo, the answer is 3.

After factoring and canceling the expression becomes

And substituting 3 for x yields

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A. 0

B. undefined

C. x 2

D. x 2 - x

E. None of the above

No that answer is incorrect.

Try factoring out an h and cancelling

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Yes, the answer is x 2

= x 2

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A. Yes

B. No

C. None of the above

No that answer is incorrect.

Find the limits as x approaches 3 from the left and from the right.

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Yes, the answer is No!

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Try to explain your answer and then click here to see if you are correct.

The Limit does not exist so it is not continuous!

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A. y’ = - 2 x- 3

B. y’ = 2 x

D. y’ = x + 3 - 5

C. y’ = 2x + 3

E. None of the above

Not quite, that answer is incorrect.

Use the definition for derivative – the five step procedure – or use the power rule.

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Hey great, the correct answer is y’ = 2x + 3

Nice work on the power rule.

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Now, let’s try some application problems.

CLICK CLICK CLICK

CLICK

22. A manufacturing company has fixed cost of $400 per day and total cost of $5,200 per day at an output of 20 items. .A. What are the variable cost? State and identify the variable cost as per day or per item.

A. $5,200 per day

- $4,800 per day.

C. $240 per item.

D. $260 per item.

E. None of the above

Sorry that answer is incorrect.

To find the variable cost subtract the fixed cost from the total cost. Remember

Total Cost = Variable Cost + Fixed Cost

so

Variable Cost = Total Cost – Fixed Cost

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Yes, the answer $4,800 per day or divide that by the 20 items produced to get $240 per item.

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23. A manufacturing company has fixed cost of $400 per day and total cost of $5,200 per day at an output of 20 items.B. Find the equation of the line relating the output to the total cost. Write your final answer in the form C (x) = mx + b.

A. C (x) = 5200 x + 400

- C (x) = 4800 x + 400.

C. C (x) = 5600 x + 400

D. C (x) = 240 x + 400

E. None of the above

No that answer is incorrect.

To find the the equation you can use the two points given (The total cost at a production level of 0 and the total cost at a production level of 20) and substitute into the slope/point form of an equation.

OR

You may remember that the slope is the per unit variable cost and the y-intercept is the fixed cost and y = mx + b.

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Yes, the answer is

C (x) = 240 x + 400.

NOTE: You will need this equation for the next question.

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24. A manufacturing company has fixed cost of $400 per day and total cost of $5,200 per day at an output of 20 items. C. What is the total cost for an output of 15 units per day?

A. C (x) = $4000

- C (x) = $4800

C. C (x) = $266.67

D. C (x) = $240

E. None of the above

Too bad that answer is incorrect.

All you need to do is substitute 15 into the correct total cost equation from the previous problem.

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Yes, the answer is

C (15) = (240)(15) + 400

= $4,000.

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25. The price-demand and cost functions for selling bicycles are:p (x) = 75 – 3x and C (x) = 125 + 16x A. What is the revenue function?

A. R (x) = 75/x - 3

- R (x) = 75x – 3 x 2

C. R (x) = 200 + 13x

D. R (x) = 125x + 16 x 2

E. None of the above

No that answer is incorrect.

The revenue equation is formed by multiplying the price equation by x. That is, revenue is the price times the number sold. R = px

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Yesaroonie, the answer is

R (x) = 75x – 3 x 2

Since

R (x) = px

= (75 – 3x) x

= 75x – 3x 2

NOTE: You will need this equation for the next question.

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26. The price-demand and cost functions for selling bicycles are:p (x) = 75 – 3x and C (x) = 125 + 16x B. What is the profit function?

A. P (x) = 200 + 13 x

- P (x) = 75x – 3 x 2

C. P (x) = - 3x 2 + 91x + 125

D. P (x) = - 3x 2 + 59x - 125

E. None of the above

No that answer is incorrect.

The profit equation is formed by subtracting the cost equation from the revenue equation. The revenue equation was found in the previous problem.

P = R - C

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Perfect, the answer is

P (x) = - 3x 2 + 59x – 125

Since

P (x) = R – C

= (75x – 3x 2) – (125 + 16x)

= 75x – 3x 2 – 125 – 16x

= - 3x 2 + 59x - 125

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A. (2.42, 163.64)

- (17.25, 401.02)

C. (3.58, 201.55)

D. (8.56, 334.87)

E. None of the above

Sorry that answer is incorrect.

Graph both equations on your calculator and find the point of intersection using CALC and INTERSECT.

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You have magic fingers on your calculator.

The correct answers are (2.42, 163.64) and

(17.25, 401.02)

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28. A company has the following revenue function, where x is in thousands, for making tee shirts with domain 0 to 20 thousand.R (x) = x(75 – 3x).A. Find the output of shirts that will produce the maximum revenue.

A. 25

- 468.75

C. 12.5

D. 333.33

E. None of the above

Not the correct answer.

Graph the equation on your calculator and find the point of maximum using CALC and MAXIMUM.

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Sorry that is not the correct answer, but it is close.

You were asked for the output. You want the x value of the maximum not the y value.

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Great calculator work.

The correct answers are 12.5 thousand tee shirts.

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29. A company has the following revenue function , where x is in thousands, for making tee shirts with domain 0 to 20 thousand.R (x) = x(75 – 3x).B. What is the maximum revenue.

A. 25

- 468.75

C. 12.5

D. 333.33

E. None of the above

Sorry incorrect. Try the following hint.

Graph the equation on your calculator and find the point of maximum using CALC and MAXIMUM.

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Sorry that is not the correct answer, but it is close.

You were asked for the output. You want the y value of the maximum not the x value.

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Great calculator work.

The correct answer is $468.75

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30. A company has the following revenue function , where x is in thousands, for making tee shirts with domain 0 to 20 thousand.R (x) = x(75 – 3x).C. What is the price per tee shirt that maximizes the revenue.

A. $25

- $468.75

C. $12.5

D. $37.50

E. None of the above.

Sorry that answer is wrong.

This problem is somewhat difficult. First, you are looking for a price so you need a price-demand equation. You can get that from the revenue equation. Remember Rev = x p so p = Rev/x or p (x) = 75 – 3x. Now use the x you found in part A (Problem 23) to find the price.

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WOW, yes a tough one!

The correct answer is $37.50

You can either take the total revenue at the maximum and divide by the x value or you can find the price-demand equation from the given revenue equation and substitute the x value you found at the maximum.

Please click here for the next question.

A. x + 2

- 2x + 12

C. - 2x + 12

D. - x 2 + 2x + 2000)

E. None of the above

Too bad, that is incorrect.

Use the power rule to find the derivative.

If y = x n , then y’ = n x n – 1 .

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Well done!

The correct answer is - 2x + 12

You will need this answer for the next question.

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31. The number of bacteria in a culture x hours after treatment is given byf (x) = - x 2 + 12 x + 1000.B. Find The instantaneous rate of change after 2 hours.

A. - 8

- 1020

C. 8

D. 1012

E. None of the above

Sorry that is incorrect.

Use the results of the previous question and substitute x = 2.

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Sorry that is not the correct answer, but it might be close.

Use the results of the previous question and substitute x = 2.

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Well done!

The correct answer 8 bacteria.

Substitute 2 into the answer of the previous question giving

- 2 (2) + 12 = - 4 = 12 = 8

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31. The number of bacteria in a culture x hours after treatment is given byf (x) = - x 2 + 12 x + 1000.C. Interpret the results of the previous problem.

Answers will vary but click here to see my answer.

In the next hour the number of bacterial will increase by about 8.

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