Chapter 2 In-Class Review

1. Let and

find h’(5)

)()()( xgxfxh

21)5(',1)5(,4)5(',2)5( ggff

2) Find an equation of the tangent line to the graph of the function at the point where x = -4

f (x) x 2 2x 5

3. Find the derivative of

f (x) x 4 7 9x

4. Differentiate

y csc4 (tan(x 2 2))

5. Find dy/dx for

tan(12x y) 12y

6. Determine the slope of the graph

9x 2 5xy 3y 2 7 0 at the point ( 1, 1)

7. A conical tank with vertex down is 16 feet across the top and 24 feet deep. Water is flowing into the tank at a rate of 14 cubic feet per minute, find the rate of change of the depth of the water when the water is 11 feet deep

8. A kite is flying 150 m high, where the wind causes it to move horizontally at a rate of 5 m per second. In order to maintain the kite at a height of 150 meters, the person must allow more string to be let out. At what rate is the string being let out when the length of the string is already out 250 m.

Alternative form of the derivative at a point

• The derivative of at point c is given by:f

cxcfxfcf

cx

)()(lim)(

9) Is differentiable at x = 1

f (x) (x 1)3, x 1

(x 1)2, x 1

limx1

f (x) f (1)x 1

limx1

(x 1)2 0x 1

limx1

f (x) f (1)x 1

limx1

(x 1)3 0x 1

1 at x abledifferenti is f(x) and exists )1( f

)1(f

10) If find

1 ,)1(2

1 ,)1(3)(

2

xx

xxxf )1('f

Homework: Page 158# 1-12 all, 15-29 odd, 41-57 odd, 73, 75, 93,

103, 104, and 107