The necessary condition to be maximum or minimum for the function is

f(x) = 0 and it is sufficient

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f"(x) = 0 and it is sufficient

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f'(x) = 0 but it is not sufficient

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f'(x) = 0 and f"(x) = -ve

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Solution

The correct option is C
f'(x) = 0 but it is not sufficient

Necessary condition for a function to have an extrema is f'(x) = 0. But it is not sufficient. Along with this f"(x) should be non zero.

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