For the curve y = 2x^2+4x+5, find the co-ordinates of the stationary point and determine whether it is a minimum or maximum point.
Stationary points occurs when the gradient of the graph is equal to 0, i.e. dy/dx = 0. Differentiate y with respect to x to get dy/dx = 4x + 4.So making 4x + 4 = 0 gives x = -1. Substituting this into the original equation for y will give the the y co-ordinate, y = 3.Finding the rate of change of the gradient at the stationary point tells us whether it is minimum or maximum. Doing this gives d2y/dx2 = 4. Since this is greater than 0 the stationary point at (-1,3) is a minimum point.
OB
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