Question

If a function $f\left(x\right)$ has $f^{\prime }\left(a\right)=0$ and $f^{\prime \prime }\left(a\right)=0,$ then

• A. $x=a$ is a maximum for $f\left(x\right)$,
• B. $x=a$ is minimum for $f\left(x\right)$,
• C. It is difficult to say $\left(a\right)$ and $\left(b\right)$,
• D. $f\left(x\right)$ is necessarily a constant function.

Answer 1

Answer: (C)

It is difficult to say $\left(a\right)$ and $\left(b\right)$,

It is fundamental concept that,
If a function $f\left(x\right)$ has $f^{\prime }\left(a\right)=0$ and $f^{\prime \prime }\left(a\right)=0,$ then
It is difficult to say $x=a$ is point of maxima or minima.