3.1 The numerical approximation to the gradient of a function f(x) for a scalar quantity x, given in Figure 3.3, is f

(x), given by:

2δf

(x) = f(x + δ) − f(x − δ).

Use Matlab to compare the performance of this method with the alternative which results in:

12δf

(x) = f(x − 2δ) − 8f(x − δ)+8f(x + δ) − f(x + 2δ).