Critical number :

A critical number of a function $\"\"$ is a number $\"\"$ in the domain of $\"\"$ such that either $\"\"$ or $\"\"$ does not exist.

$\"\"$

The derivative of a function is $\"\"$ .

The solutions of $\"\"$ are the critical numbers.

Equate $\"\"$ to zero :

$\"\"$

It is hard to find the solution for the above equation numerically.

Hence we find the number of solutions of the function graphically.

$\"\"$

Graph :

Graph the equations $\"\"$ and $\"\"$ .

$\"\"$

Observe the graph.

The intersecting points are the solutions.

Thus, the function $\"\"$ has $\"\"$ critical numbers.

$\"\"$

The function $\"\"$ has $\"\"$ critical numbers.

$\"\"$ .