Question

According to mean value theorem in the interval $x\in \left[0,1\right]$ which of the following does not follow-

• A. $f\left(x\right)=\{\begin{array}{c}\frac{1}{2}-xx<\frac{1}{2}\\ {\left(\frac{1}{2}-x\right)}^2,x\ge \frac{1}{2}\end{array}$
• B. $f\left(x\right)-\{\begin{array}{c}\frac{\sin x}{x};x\ne 0\\ 1;x-0\end{array}$
• C. $f\left(x\right)-x\left|x\right|$
• D. $f\left(x\right)=\left|x\right|$

Answer 1

The correct option is A $f\left(x\right)=\{\begin{array}{c}\frac{1}{2}-xx<\frac{1}{2}\\ {\left(\frac{1}{2}-x\right)}^2,x\ge \frac{1}{2}\end{array}$