After defining the three functions above, compute the finite difference approximation of for decreasing values of the perturbation dx stored in the 1d numpy array dxvec. For each perturbation dx, compute the error between the approximated and exact derivative. This result should be an array. Compute the infinity p-norm of this array. Store this result in the variable error, which should have the same shape as the array dxvec. Plot the error as a function of the perturbation size. What do you observe