Derivative Calco

25y x

16

A stone is thrown upward from the top of a building that is 304 feet high

with an initial velocity of 80 ft/sec.(a)What is the maximum height of the stone?(b) What is the velocity of the stone just prior

to striking the ground?

2 14

20

sin( ) '( )

(1- cos )

xf x find f x

x

2 2x xy

x

4

4 31

3y x

x

13 23

f(x) = 5secx + tanxfind f’(x)

24

2 39 1 1y x x

29 7

3 2

2 1Find 7

' 3 49

'' 3 24

f x x ax bx c

ff

f

f

18

12

5

xxy

x

11 27

3 22 115 7

3 2y x x x

For what values of x will the curve,

have a positive slope?

35

10 33

f(x) = 6xsecx – 2cosx

find f’(x)

A woman on top of a building throws a ball up in the air.

Two seconds after she throws it, the ball is 412 ft above

the earth traveling 24 ft/sec. How tall is the building?

21

2

3

4x xy

x

5 26

Suppose the position of a moving object is

23 2 5s t t t , where s is measured in meters and t is measured in seconds.

(a) Find the average velocity of the object between 1 and 2 seconds.

(b) Find the instantaneous velocity when t =1 and t = 2.

19 31

Find the equation of the tangent line to

3sin3

f x x at x

1 30

1

2

xf x

x

''f xFind

17 32