9. Let f(x) = 2sin x. Then f"(0) =
|
A. –ln 2 |
B. –(ln 2)2 |
C. 0 |
|
D. (ln 2)2 |
E. ln 2 |
Solution: The answer is D
First, taking logs,
Consequently,
or
Differentiating again,
Since f(x)=2sin(x) , f(0) = 20 = 1. Since f'(x) = cos(x)ln(2)f(x), f'(0) = ln(2). Consequently f''(0) = ln(2)*ln(2).