The necessary condition for a function to hav | vedclass

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(C) For a function $f(x)$ to have a local maximum or minimum at a point $x = c$,the first derivative $f'(c)$ must be equal to $0$. This is known as th

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

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(C) For a function $f(x)$ to have a local maximum or minimum at a point $x = c$,the first derivative $f'(c)$ must be equal to $0$. This is known as the first-order necessary condition. However,$f'(x) = 0$ alone is not sufficient to guarantee a maximum or minimum,as it could also be a point of inflection. To confirm the nature of the extremum,we use the second derivative test: If $f''(c) If $f''(c) > 0$,the function has a local minimum at $x = c$. Therefore,$f'(x) = 0$ is a necessary condition but it is not sufficient.

The necessary condition for a function to have a maximum or minimum value is:

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