Given f(x)=2x^3 - 2x^2 + 8x, find f'(x) and f"(x).
The first step in scoring full marks on this typically 4 mark question is to recognise what it's asking you to do. We use the process of differentiation to solve it. f(x)=2x^3 - 2x^2 + 8xf'(x) = 6x^2 - 4x + 8 as we multiply coefficients by the corresponding power of x and then reduce the power by 1. This also leaves the final term as a constant term without an x. The general rule we use is f'(x) = (na)x^(n-1) where our original equation has the form f(x) = ax^n.Using a similar method for f"(x) where the question asks us to differentiate again to find the second derivative, we find f"(x) = 12x - 4.
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