For the curve f(x) = 2x^3 - 54x, find the stationary points and state the nature of these points
Firstly, find the values of x where f'(x) = 0
f'(x) = 6x2 - 54
6x2 - 54 = 0
6(x+3)(x-3) = 0
x = 3, y = -108 and x = -3, y = 108
Next, find the values of f''(x) at these points
f''(x) = 12x
When x = 3, f''(x) = 36 which is positive and therefore (3,-108) is a minima.
When x = -3, f''(x) = -36 which is negetive and therefroe (-3,108) is a maxima.
