If for a function f(x),f'(a) = 0 and f''(a) = | vedclass

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(C) For a function $f(x)$,the condition $f'(a) = 0$ and $f''(a) = 0$ is a necessary condition for a point of inflection,but it is not sufficient to co

Vedclass · Accepted Answer

Not an extreme point

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(C) For a function $f(x)$,the condition $f'(a) = 0$ and $f''(a) = 0$ is a necessary condition for a point of inflection,but it is not sufficient to conclude that $x = a$ is an extreme point (a local maximum or minimum). If $f'(a) = 0$ and $f''(a) = 0$,the point $x = a$ could be a local maximum,a local minimum,or a point of inflection (like in $f(x) = x^3$ at $x = 0$). Therefore,without further information about higher-order derivatives or the sign change of $f'(x)$ around $a$,we cannot definitively classify it as an extreme point. Thus,the most accurate general statement among the choices is that it is not necessarily an extreme point.

If for a function $f(x)$,$f'(a) = 0$ and $f''(a) = 0$,then $x = a$ is:

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