Question

Answer the following question in one word or one sentence or as per exact requirement of the question.
Write necessary condition for a point $x=c$ to be an extreme point of the function $f\left(x\right)$.

Answer 1

Given function,

$f\left(x\right)$

Given, $x=c$

$\Rightarrow f\left(x\right)=f\left(c\right)$

derivating the function,

$f^{\prime }\left(c\right)=0$

Hence the condition