A curve has equation y = x^3 - 6x^2 - 15x. The curve has a stationary point M where x = -1. Find the x-coordinate of the other stationary point on the curve.
A stationary point can be found when dy/dx = 0. The first thing we need to do is differentiate y to find dy/dx, and solve it for dy/dx = 0. This gives usdy/dx = 3x2 - 12x - 15 = 0 = (3x + 3)(x - 5) = 0 (using quadratic formula)Therefore x = -1 and x = 5.The question already gives us x = -1, so the answer is x = 5.
