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.