Find the stationary points of the function f(x) = x^3 - 27x and determine whether they are maxima or minima
A stationary point occurs when the first derivative of the function = 0. The first derivative of f(x) is df(x)/dx = 3x^2 - 27Setting this to zero gives 3x^2 - 27 = 0 -> x = +/- 3
To find whether it is a maxima or minima we find the second derivative d^2 f(x)/dx^2 at 3 and -3d^2 f(x)/dx^2 = 6x d^2 f(x)/dx^2 when x = 3 -> 18As a rule, when the second derivative > 0, the point is a minimumd^2 f(x)/dx^2 when x = -3 -> -18As a rule, when the second derivative < 0, the point is a maximum
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