Question

The first and second order derivatives of a function f(x) exist at all points in (a,b) with
$f^{\prime }\left(c\right)=0$, where $a<c<b$. Further more, if $f^{\prime }\left(x\right)<0$ at all points on the immediate left of $c$ and $f^{\prime }\left(x\right)>0$ for all points on the immediate right of $c$, then at $x=c,f\left(x\right)$ has a

• A. local maximum
• B. local minimum
• C. point of inflexion
• D. none of these

Answer 1

Answer: (B)

local minimum

Since, f'(x) changes from negative to positive.
So, f(x) has a local minimum at $x=c$