Derivatives, Antiderivatives, and Indefinite Integrals

Chapter Three -- Test One Review

Use the given graph of f for 1–4 1) f ΄(x) = 0 when x =

2) f ΄(x) = 0 does not exist when x =

3) f ΄(x) < 0 when x =

4) f ΄(x) > 0 when x =

5) Sketch f ΄(x)

6) 3 3

0

2( ) 2limh

x h x

h

7) If f (x) = 6x2 + x-2 , then f ΄(4) =

8) If f (x) = 6x1/3 + 8x-1/4 + 8 , then f ΄(x) =

9) Given f (x) = 3x2 – 4x + 2 , 1) State f ΄(x) =

2) Use a definition to prove.

9) If f (x) = -3x4 + 8x5/4 , then 2

2

d y

dx

11) Sketch the graph of f (x) = 2x3 + 4x2 – 4x – 2

and f ΄(x).

If f (x) = 2x3 + 4x2 – 4x – 212) Find f ΄(x)

If f (x) = 2x3 + 4x2 – 4x – 212) Find the set of values of x for which f ΄(x) = 0

are

If f (x) = 2x3 + 4x2 – 4x – 2

12) Determine where f (x) is increasing.

If f (x) = 2x3 + 4x2 – 4x – 212) Determine where f ΄(x) is negative.

If f (x) = 2x3 + 4x2 – 4x – 212) State the ordered pair for all local extrema of

f (x). Justify your answer with calculus.

Let x(t) = 4t3 – 16t2 + 12t t 0a) Determine the velocity of the particle at

time t.

Let x(t) = 4t3 – 16t2 + 12t t 0b) Determine the acceleration of the particle at

time t.

Let x(t) = 4t3 – 16t2 + 12t t 0c) Is the particle speeding up or slowing down

at t = 1? Explain your reasoning.

Let x(t) = 4t3 – 16t2 + 12t t 0d) When is the particle at rest?

Let x(t) = 4t3 – 16t2 + 12t t 0e) When is the particle moving to the right?

Justify your answer.

Let x(t) = 4t3 – 16t2 + 12t t 0f) Determine all local maximums and minimums

of the position function.