A right triangle has one vertex on the graph of y = 9 - x^2, where x > 0, at point (x, y), another at the origin and the third on the positive x-axis at point (x, 0). Express the area A of the triangle as a function of x.
A right triangle has one vertex on the graph of y = 9 - x^2, where x > 0, at point (x, y), another at the origin and the third on the positive x-axis at point (x, 0). Express the area A of the triangle as a function of x.
It is the height of the triangle which is $\displaystyle y$ which is $\displaystyle 9-x^2$ times the base of the triangle with is $\displaystyle x$ times 1/2.
Thus,
$\displaystyle \frac{1}{2}x(9-x^2)$