Question

If $y=f\left(x\right)$ is a polynomial function and graph of $y=f^{\prime }\left(x\right)$ in interval $(1,8)$ is shown in figure below, then consider the following data in interval $(1,8)$

If $a$ = number of point(s) where $y=f\left(x\right)$ has maxima
$b$ = number of point(s) where $y=f\left(x\right)$ has minima
longest interval of $y=f\left(x\right)$ is decreasing is $(m,n)$ then value of $(m+n+a+b)$ is

Answer 1

maxima at $x=1\Rightarrow a=1$
minima at $x=3\Rightarrow b=1$
$y=f\left(x\right)$ decreases in $(1,3)$
So $m=1,n=3$
So $(m+n+a+b)$ is $6$.