Question

Let $f\left(x\right)$ be differentiable function in $[2,7]$. If $f\left(2\right)=3$ and $f^{\prime }\left(x\right)\le 5$ for all $x$ in $(2,7)$, then the maximum possible value of $f\left(x\right)$ at $x=7$ is

• A. $7$
• B. $15$
• C. $28$
• D. $14$

Answer 1

The correct option is C $28$

Now, its given that $f^{\prime }\left(x\right)\le 5$

$\frac{k-3}{7-2}\le 5$ ($f\left(x\right)=$ slope $=\frac{y_2-y_1}{x_2-x_1}$)

$k-3\le 25$

$k\le 28$

Therefore, maximum possible value of $f\left(x\right)$ at $x=7$ is $28$