A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.
We know that a stationary point is found when the gradient of the curve is equal to zero, this is found by equaling the derivative (dy/dx) equal to zero. Differentiating the expression will find a quadratic that can be factorised into two brackets, the two brackets represent the two co-ordinates of the two stationary points, one of which will be P=-2 and the other is found to be x=5/3.The second derivative of the expression can be found, and when P is substituted in, a value is found which represents if it is a maximum or minimum value of the curve. This is found to be d2y/dx2 = 22, which is a positive value and therefore a minimum curve point.
