Let x and y be real numbers such that 0 <= x <= 1 and 0 <= y <= 1. Find the maximum value of x^2 - y^2.
You need y² to be as small as possible and x² to be as large as possible. You can set y to 0 to make y² as small as possible. You want x to be as big as it can possibly be, which happens to be 1, in this case. Doing the calulculations result in 1² - 0² = 1 - 0 = \(1\).