Question: Explain why the condition f'(x)=0 is necessary but not sufficient for x to yield a maximum of f, while f'(x)=0 and f''(x) < is sufficient

Explain why the condition f'(x*)=0 is necessary but not sufficient for x* to yield a maximum of f, while f'(x*)=0 and f''(x*)< is sufficient but not necessary for x* to yield a maximum.

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Question: Explain why the condition f'(x*)=0 is necessary but not sufficient for x* to yield a maximum of f, while f'(x*)=0 and f''(x*) < is sufficient

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Question: Explain why the condition f'(x)=0 is necessary but not sufficient for x to yield a maximum of f, while f'(x)=0 and f''(x) < is sufficient