2 Consider the function fa 2 4 on the interval 221 with h 02

2. Consider the function: f(a) 2- 4 on the interval (-2,21 with h 0.25. Use the forward, backward, and centered finite difference approx- imations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well.

Solution

f(x)= x3 _2.x +4

Calculus:

>> syms x;

>> diff(x^2)

ans =2*x

2.     

>> syms x

>> diff(x^4)

ans = 4*x^3

diff(x3 _2.x +4)

>> syms x;
diff(x^3-2*x+4)

ans =

3*x^2 - 2

diff(3*x^2 - 2)

>> diff(3*x^2 - 2)

ans =

6*x