Question

A curve has equation y = x²(x - 2) Work out the gradient of the curve at the point (3,9).

Answer 1

Answer:

y = x^2 (x - 2) = x^3 - 2 x^2

dy/dx = 3 x^2 - 4 x

At x = 3  dy/dx = 3 * 9 - 4 * 3 = 15  The slope (gradient) of the curve