3. Let the functions f, g, and h be defined as follows:
Which of these functions are differentiable at 0?
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A. None |
B. f and g only |
C. f and h only |
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D. g and h only |
E. The correct answer is not given by A, B, C, or D. |
Solution: The answer is D
By definition, a function f is differentiable at 0 if f’(0) exists. Thus, the derivative of the above functions evaluated at zero are given by:
Since, g’(0) and h’(0) are the only derivatives that exist, then g and h are the only functions that are differentiable at zero.