Find the stationary points of y = x^3 -3x^2 - 9x +5

A stationary point is a point where dy/dx = 0.First we need to find dy/dx. This is done by differentiating y term by term to get dy/dx = 3x^2 - 6x - 9.Setting this equal to zero, we need to solve 3x^2 - 6x - 9 = 0.This equation can be simplified by dividing both sides by 3.So we need to solve x^2 - 2x - 3 = 0.Completing the square, we get (x - 1)^2 - 4 = 0.Add 4 to both sides to get (x - 1)^2 = 4.We see that x = 3, x = -1 are the two solutions. Now to find the y values, we must sub in x = -1 and x = 3 into y = x^3 - 3x^2 - 9x + 5.For x = 3, we get y = --22, and for x = -1, we get y = 10.So the two stationary points are (3,-22) and (-1,10)