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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
slide1

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

slide2

Formula for surface area of a rectangular box that has a square base with side length x and height y

slide4

If

Then when , and t = 1

slide8

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?

slide10

A snowball melts at a rate of cubic inches per hour. What is the rate that the radius is changing when the snowball has diameter 6 inches?

Volume of sphere

slide12

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

critical number a number c is a critical number of a function f x if f c is either 1 or 2

Critical NumberA number c is a critical number of a function f(x) if f’(c) is either (1.)______ or (2.)______.

slide16

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.)________

slide18

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
(1.) local minimum

(2.) local maximum

fundamental theorem of calculus part ii let f x be a continuous function on a b then 1
Fundamental Theorem of Calculus, Part II

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

(1.)_____

slide32

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).

slide34

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.

slide38

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?

slide40

What are the relevant variables if the problem is to find a right circular cone of surface area 20 and maximum volume?

find s t if

Find s(t)if

and s’(0)=1, s(0)=10

slide51

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?