How do you find the maximum in a math problem?

Answer 1

It depends on the function whose maximum you are trying to find.

If it is a well behaved function over the domain in question, you could differentiate it and set its derivative equal to 0. Solve the resulting equation for possible stationary points.

Evaluate the second derivative at these points and, if that is negative, you have a maximum. If the second derivative is also 0, then you have to go to higher derivatives (if they exist).

If the function is not differentiable, you may have a more difficult task at hand.