Question

Suppose $f$ is a continuous function and $f^{\prime}(x)$ exists everywhere. If $f(2)=10$ and $f^{\prime}(x) \geq-3$ for all $x$, then the smallest possible value for $f(4)$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

For minimum value of $f (4)$
$\frac{ f (4)- f (2)}{4-2}=\min \left( f ^{\prime}( x )\right) $
$\Rightarrow f (4)- f (2)=2 \cdot(-3) $
$\Rightarrow f (4)=-6+10=4$