Question

The graph of the function $y=f\left(x\right)$ is given below

Then which of the following is/are true

• A. $f^{\prime }\left(x\right)<0$ if $0<x<2$
• B. $f^{\prime }\left(x\right)>0$ if $0<x<2$
• C. $f^{\prime \prime }\left(x\right)>0$ if $0<x<1$
• D. $f^{\prime \prime }\left(x\right)<0$ if $1<x<2$

Answer 1

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

$f^{\prime \prime }\left(x\right)<0$ if $1<x<2$

From the graph, it is clear that
$f\left(x\right)$ is increasing in $[0,2]$
$\Rightarrow f^{\prime }\left(x\right)>0$ if $x\in [0,2]$
Also, $f\left(x\right)$ is concave up in $(0,1)$ and concave down in $(1,2)$
$\therefore f^{\prime \prime }\left(x\right)>0$ if $0<x<1$
and $f^{\prime \prime }\left(x\right)<0$ if $1<x<2$