Question

How do you find all local maximum and minimum points using the second derivative test given `y=tan^2x`?

Answer 1

graph{(tanx)^2 [-7.09, 12.91, -2.12, 7.88]}

It has minimum at `x=kpi, kinZZ` valued 0

Explanation:

`y'=2(tanx)/cos^2x`

`y'=0, AAx=kpi, kinZZ`

`y''=2*(1/cos^2x*cos^2x+2tanxcosxsinx)/(cos^4x)=2*(1+2sin^2x)/cos^4x>0, AAx inRR`

So the critical points in `kpi` are local minimum.