Question

Let $f\left(1\right)=-2$ and $f^{\prime }\left(x\right)\ge 4.2$ for $1\le x\le 6$. The smallest possible value of $f\left(6\right)$ is

• A. $9$
• B. $12$
• C. $15$
• D. $19$

Answer 1

Answer: (D)

$19$

By Lagrange's mean value theorem,
$\frac{f\left(6\right)-f\left(1\right)}{6-1}=f^{\prime }\left(c\right)$
$\frac{f\left(6\right)+2}{5}\ge 4.2$
$f\left(6\right)+2\ge 21$
$f\left(6\right)\ge 19$