Question

Let $f$ be differentiable for all $x$. If $f\left(1\right)=-2and{f}^{\prime }\left(x\right)\ge 2$ for $xϵ[1,6]$ then the value of $f\left(6\right)$ is

• A. Less than $8$
• B. greater than or equal to $8$
• C. equal to $5$
• D. Less than $5$

Answer 1

The correct option is B greater than or equal to $8$

Let take least possible case than function would be straight line.
$(y_2-y_1)=m(x_2-x_1)$
$(y_2+2)=2(6-1)=y_2=8$
So $f\left(6\right)$ will be $8$ or greater than $8$.