1. Tardigrade
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  4. A point c in the domain of a function f is called a critical point of f if (i) f prime(c)=0. (ii) f is not differentiable at c.

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Q. A point $c$ in the domain of a function $f$ is called a critical point of $f$ if
(i) $f^{\prime}(c)=0$.
(ii) $f$ is not differentiable at $c$.

Application of Derivatives

Solution:

A point $c$ in the domain of a function $f$ at which either $f^{\prime}(c)=0$ or $f$ is not differentiable is called a critical point of $f$. Note that if $f$ is continuous at $c$ and $f^{\prime}(c)=0$, then there exists an $h>0$ such that $f$ is differentiable in the interval $(c-h, c+h)$.