A curve has equation y = x^3 - 48x. The point A on the curve has x coordinate -4. Is A a stationary point?

A stationary point indicates that the gradient at that coordinate is 0. Hence we need to find the gradient of the line, set this to 0, and then substitute our value of x. Find dy/dx. Remember the equation for the gradient of the curve y = x^3 - 48x. Differentiation involves two steps which must be performed in the following order. If they are not performed in this order you WILL get a different result. The first step is to bring the power down to the front. Followed by reducing the power by 1. These must be done in the right order. Hence, dy/dx = 3x^2 - 48. We are told in the question that x = -4 at this point on the curve. Therefore we need to substitute -4 into the equation. Gives: 3(-4)^2 - 48 = 0. Hence gradient = 0 at this point verifies that A is a stationary point.