Question

If $f\left(x\right)$ is a differentiable function, $f^{\prime }\left(x\right)\ge 2,forallx\in R,f\left(1\right)=2$, then possible value of $f\left(3\right)$ are

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (B), (C), (D)

The correct options are
B 6
C 7
D 8

$\frac{f\left(3\right)-f\left(1\right)}{3-1}=f^{\prime }\left(c\right)$, for some $c$ such that 1 < c < 3
$f^{\prime }\left(c\right)=\frac{f\left(3\right)-2}{2}\ge 2$
$\therefore f^{\prime }\left(3\right)\ge 6$
Therefore, possible answers could be $6$, $7$ and $8$.
Hence, option 'B', 'C' and 'D' are correct.