Review Test 2

1. If G(x) = f(2f(2f(x))), where f(0) = 0 and f’(0) = 2, Find G’(0).(A) 0 (B) 23 (C) 24 (D) 25 (E) None of the above

2. Find an equation of the tangent line to the curve y = f(x) at the point when x = 2018.

(A) y = 2018 + f ’(2018)(x - 2018) (B) y = 2018 + f ‘(2018)x (C) y = f ‘(x)(D) y = f(2018) + f’(2018)(x - 2018) (E) None of the above

3.Which one of the following statements is true?(A) If f(x) = sin(1), then f’(x) = cos(1).(B) If f and g are differentiable, then [f(x)g(x)]’ = f’(x)g’(x).(C) If y = e8, then y’ = 8e7.(D) The derivative of 84x 4x ln 8 ln 4

(E) ddx

(10x)=x10x−1

4.The table below gives several values for the function f and its derivative f.

If p(w) = f(f(-w + 1)), then p’(1) is,a)0.5b)1.5c)-1.5d)-1e)0

5)Consider the graphs of f(x) and g(x) below. Let h(x) = f(g(x)), then h’(30) =

a)0b)20c)30d)40e)does not exist

6) The function f(x) = 2 x3+ 300x3 +4

a)increasing at x = -2b)decreasing at x = -2c)constant at x = -2

7) The graph of f(x) is given below:For which of the following is f’(x) > 0 ?

a)x = -5b) x = -1c)x = 1.5d)x = ee)None of these

8) Let f(x) = cos(2x). Find the points at which the tangent line is horizontal for 0≤ x≤2 pi

9) True or false : If f is a function that is differentiable at a, then the linearization L(x) = f(a)+f’(a)(x-a) can be used to find the exact value of f(x) when x is near a.

10) Find the derivative of g(x) = √ ln (√x )

11) The table below gives several values of a differentiable function f(x).Let h(x) = f(e^x). Then h’(ln 2) =

a)-6b)0.6c)2d)4e)6

12) 13) If f(x) = ax^3 + a^2 and f’’(2) = -6 then what is the value of a?

a)0.5b)-0.5c)-2d)2

e)None of the above

14) If f(x) = pi^5, then f0(x) = 5pi^4

a)Trueb)Falsec)Cannot be determined