Question

How do you find the slope of the tangent line to the graph `f(x)=sin ^2x` when `x=pi`?

Answer 1

The answer is: `0`.

Since the slope of the tangent line to a graph in a point is the derivative in this point:

`y'=2sinxcosxrArr`

`y'(pi)=2sinpicospi=2*0*(-1)=0`

In fact in `x=pi` there is a local minimum, as you can see:

graph{(sinx)^2 [-10, 10, -5, 5]}