Question

How can i find the critical point of tanx? help me

Answer 1

There are no critical points.

Explanation:

A critical point is a point in the domain of `f(x)` at which `f'(x)` is 0 or undefined.

For `f(x)=tan(x)` we have `f'(x)=sec^2(x)`.

`sec(x)` is never equal to 0 so we have to find where `sec(x)` is undefined. This will happen every time `cos(x)=0` because `sec(x)=1/cos(x)`.

`cos(x)=0\rightarrow x=pi/2 +pi*n`, `n in ZZ`.

Now the issue is that every time `cos(x) = 0` tangent is undefined so those values are not in the domain. There are no critical points of `tan(x)`.