text 3 consider the function f x 0 1 x 4 0 15 x 3 0 5 x 2 0 25 x 1 2 t

Question

\text { 3. Consider the function } f(x)=-0.1 x^{4}-0.15 x^{3}-0.5 x^{2}-0.25 x+1.2 \text {. } (a) Obtain the analytical expression (i.e. True or Exact Solution) for the first derivative, . Evaluate its value at a 0.5. Box your answer and label it as faxact.
c) In MATLAB, plot e versus the grid spacing (i.e. e on vertical axis and h on the horizontal axis)on a log - log plot. (A log – log plot does not mean taking the logarithm of these values, butthe scales are logarithmic.). i. What happens to the error as step size decreases? Does it decrease with decreasing h? Isthe curve mostly linear for majority of the data? ii. The error versus grid spacing on log-log scale, indicates how the error changes with respect to the spacing, which is related to the order of accuracy. Find the order of accuracy of the formula using the slope of the curve in the region of decreasing error with step size.