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definition of derivative

Let
f(x)={(x^3)cos(1/x) if xâ? 0, 0 if x=0,
and
g(x)={(1/x)sin(x) if xâ? 0, 0 if x=0.

a) Using the definition of the derivative show that f is differentiable at 0 and determine f '(0).
b) Is g differentiable at 0? Justify your answer.
c) Show that f ' ^(x) and g ' ^(x) exist for xâ? 0 and determine their values.

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Solution Summary

This solution shows how to use the definition of derivative to show that given variables are or are not differentiable at 0.

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