Question

What are the extrema of `f(x)=-sin^2(ln(x^2))-cos^2(ln(x^2))` on the interval `[0,2pi]`?

Answer 1

Factoring out the negative:

`f(x)=-[sin^2(ln(x^2))+cos^2(ln(x^2))]`

Recall that `sin^2theta+cos^2theta=1`:

`f(x)=-1`

`f` is a constant function. It has no relative extrema and is `-1` for all values of `x` between `0` and `2pi`.