Applications Of Derivatives Question 306

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

Options:

A) $ f’(x)=0 $ and it is sufficient

B) $ f’’(x)=0 $ and it is sufficient

C) $ f’(x)=0 $ but it is not sufficient

D) $ f’(x)=0 $ and $ f’’(x)=-ve $

Show Answer

Answer:

Correct Answer: C

Solution:

The necessary condition to be maximum or minimum for function $ {f}’(x)=0 $ and for maximum $ {f}’’(x)=-ve $ and for minimum $ {f}’’(x)=+ve $ .

Hence $ f’(x)=0 $ , but it is not sufficient.