# Find the maximum value of the function

So I was just messing around with finding the maximum and minimum values of functions, and I came across this:

$$\text{Find the maximum value of} \,\, f(x)=\frac1{x^{2x^2}}.$$

Any ideas?

• what domain? there are several ways how one could approach this problem, one is certainly to study the derivative - you could also start by plotting the function and get some intuition May 1 '16 at 10:45

Hint. Assume $x>0$. Then you get $$f'(x)=\frac{-2x\times (1+2 \ln x)}{x^{2 x^2}} .$$ Can you take it from here?