How do I maximise/minimise a given function f(x)?

To find an extreme point of a function you must first take the derivative of f(x) with respect to x.
As the function will peak/trough at the extreme point, the gradient at this point will be equal to 0 and therefore f'(x) = 0 must be solved in order to find the value of x that maximise/minimise this function.
To check if the function is a minimum or a maximum you must take second order derivatives; f''(x).if f''(x) is negative, the found x value maximises the functionif f''(x) is positive, the found x value minimises the function