A curve has equation y = 20x -x^(2) - 2x^(3). The curve has a stationary point at the point M where x = −2. Find the x coordinates of the other stationary point.
First you must differentiate the given equation. This give you 20-2x-6x2. Since we are told that one of the stationary points is at x=-2, this is one of the factors of the differential equation. Meaning that the differential equation fully factorised is (10-6x)(2+x) =0.Wherever the differential equation has a solution pertaining to 0, this is a stationary point of the original curve. Hence x = 5/3 is the x coordinate of the second stationary point.
