# JEE Main & Advanced Mathematics Applications of Derivatives Properties of Maxima and Minima

## Properties of Maxima and Minima

Category : JEE Main & Advanced

(i) Maxima and minima occur alternately, that is between two maxima there is one minimum and vice-versa.

(ii) If $f(x)\to \infty$as $x\to a$ or $b$ and $f'(x)=0$ only for one value of $x$ (say $c$) between $a$ and $b,$ then $f(c)$ is necessarily the minimum and the least value.

If $f(x)\to -\infty$ as $x\to a$ or $b,$ then $f(c)$ is necessarily the maximum and the greatest value.

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