Mathematics - Application of Derivative Question with Solution | TestHub

Paragraph:Read the following passage and answer the questions. For every function $f(x)$ which is twice differentiable, these will be good approximation of ${\int }_a^{b}f(x)dx\cong \left(\frac{b-a}{2}\right)\{f(a)+f(b)\}$. Now, if we take $c=\frac{a+b}{2}$, then using above again, we get ${\int }_a^{b}f(x)dx={\int }_a^{c}f(x)dx+{\int }_c^{b}f(x)dx\cong \frac{b-a}{4}\{f(a)+f(b)+2f(c)\}$ and so on. We get approximation for value of ${\int }_a^{b}f(x)dx$.Question:If $f^{\prime \prime }(x)<0,\forall x\in (a,b),c(c,f(c))$ is point of maxima where $c\in (a,b)$, then $f^{\prime }(c)$ is