5. Let f(x) = sin(x)/x for x not equal to zero, and f’(0) = 1. What is f"(0)?

 

A. –2/3

B. –1/3

C. 0

D. 1/2

E. Does not exist

 

Solution: The answer is B

Start with the series for sin(x):

Thus

So

and

Consequently, f''(0) = -1/3.