Question

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 $c$.

• A. Either (i) or (ii)
• B. Only (i)
• C. Only (ii)
• D. Neither (i) nor (ii)

Answer 1

Answer: (A)

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 $(c-h,c+h)$.