Question

(iii) If $f^{\prime \prime }\left(x\right)<0\forall xϵ(a,b)$ and $(c,f\left(c\right))$ is a point lying on the curve $y=f\left(x\right),$ where $a<c<b$ and for that value of $c,F\left(c\right)$ has a maximum, then $f^{\prime }\left(c\right)$ equals

• A. $\frac{f\left(b\right)-f\left(a\right)}{b-a}$
• B. $\frac{2}{b-a}\{f\left(b\right)-f\left(a\right)\}$
• C. $\frac{2f\left(b\right)-f\left(a\right)}{2b-a}$
• D. $0$

Answer 1

The correct option is A $\frac{f\left(b\right)-f\left(a\right)}{b-a}$

it clear from theorem.