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# 200 - PowerPoint PPT Presentation

Are we r elated?. What the ________. The Highs, The Lows. Best Possible Category. Upping The Anti. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500.

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Presentation Transcript

Are we

related?

What the

________

The Highs,

The Lows

Best Possible

Category

Upping The

Anti

100

100

100

100

100

200

200

200

200

200

300

300

300

300

300

400

400

400

400

400

500

500

500

500

500

### If

Then when , and t = 1

### If and find when x=4.

A ladder 10 feet long rests against a vertical wall. If the ladder slides away from the all at a rate of 1ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet from the wall?

Volume of sphere

### 1 in/hour

Extreme Value TheoremIf f is (1.)_______ on a (2.)______ interval, then f attains an absolute maximum and an absolute minimum on the interval.

### (1.) 0(2.) undefined

First Derivative Test

If c is a critical number of a continuous function f, then:

If f’ changes from + to – at x=c, then f(c) is a (1.)_______

If f’ changes from – to + at x=c, then f(c) is a (2.)________

### (1.) local maximum(2.) local minimum

Second Derivative TestIf f’(c) = 0 and f”(c) > 0, then f has a (1.)________ at x=c. If f’(c) = 0 and f”(c) < 0, then f has a (2.)________ at x=c.

(1.) local minimum

(2.) local maximum

Fundamental Theorem of Calculus, Part II

Let f(x) be a continuous function on [a,b]. Then

(1.)_____

### interval (0, 1)

A box will be made by cutting out equal corners from four sides of a 12” by 26” piece of cardboard and folding up the sides. Write an expression for the volume of the resulting box (including the domain).

### V(x) = x(12-2x)(26-2x)and [0,6] is the domain.

5000 square inches of paper are to be used to make a poster with margins 2” on top and bottom and 3” on the sides. Draw a picture and write an expression (in one variable only) for the printed area of the poster.

### absolute maximum of 0 at x=0 and x=3absolute minimum of -1 at x=1

The problem is to find the right triangle of perimeter 10 whose area is as large as possible. What is the constraint equation relating the base b and the height h of the triangle?

### Find s(t)if

and s’(0)=1, s(0)=10

### Evaluate

A car is traveling at 40 ft/s when the brakes are fully applied, producing a constant deceleration of 20 ft/s2. What is the distance traveled before the car comes to a stop?