Question

How do you find the maximum of `f(x) = 2sin(x^2)`?

Answer 1

The maximum value of `f(x)=2sin(x^2)` is `2`.

This is an example of a kind of problem sometimes asked in a calculus class. It is a kind of a trap question. You do not need calculus to answer this question.

The maximum value of the sine function is `1`. This happens when `x^2=pi/2+2 pi k` for any integer `k`.

I also know that `x^2= pi/2` when `x=sqrt(pi/2)`.

So the maximum value of this function is `2`.

If you need to know where else the maximum occurs, then you need to solve: `x^2=pi/2+2 pi k=pi/2 (1+4k)` for any integer `k`.

The solutions are `x=+-sqrt(pi/2)sqrt (1+4k)` which might be easier to read written: `x=+-sqrt (1+4k)sqrt(pi/2)` for any integer k.