Question

Let $f\left(x\right)$ be continuous on $\left[0,4\right]$,differentiable on $\left(0,4\right).f\left(0\right)=4$ and $f\left(4\right)=-2.$ If $g\left(x\right)=\frac{f\left(x\right)}{x+2}.$ then the value of $g^{\prime }\left(c\right)$ for some lagrange's constant $c\in \left(0,4\right)$ is

• A. $\begin{array}{c}\frac{1}{2}\end{array}$
• B. $\begin{array}{c}\frac{5}{12}\end{array}$
• C. $\begin{array}{c}-\frac{5}{12}\end{array}$
• D. $\begin{array}{c}-\frac{7}{12}\end{array}$

Answer 1

Answer: (D)