Question

Let $f:IR\to IR$ be defined as $f\left(x\right)=\left|x\right|+|x^2-1|$.The total number of points at which f attains either a local maximum or local minimum is

Answer 1

Using Graph we have to check the nature of graph,
$f\left(x\right)=\left|x\right|+|x^2-1|=\left|x\right|+|x-1||x-1|$ on the interval
$(-\infty ,-1);(-1,0);(0,1);(1,\infty )$.The graph follows,
Clearly we can see that there are 2 points of local maximum and 3 local minimum i.e total 5 points.