mathematical model functions

Question

A right triangle has one vertex on the graph y=9x-x^2, x>0, at (x,y), another at the origin, and a third at the positive x-axis at (x,0). Express the area A of the triangle as a function of x.

Answer 1

The altitude of the triangle is 9x - x² and the base is x.

The area of the triangle is thus (9x² - x³)/2 for 0≤x≤9