Answer:
Answer has explained below.
Step-by-step explanation:
Consider the function is:
F(x) = 25x3 – 6x2 +7x -88
Differentiate with respect to x, we get
F’(x) = 25. 3x2 – 6.2x + 7
= 75x2 – 12x +7
At x = 2, we have
F (2) = 25(2)3 – 6(2)2 + 7(2)-88
=102
And f’(2) = 75(2)2 – 12 (2) +7
=283
Now, calculate forward divided difference as:
xi + 1 = xi + h
=2 + 0.25
=2.25
F (xi + 1) = f (2.25) = 25 (2.25)3 – 6(2.25)2 +7(2.25) -88
=182.21
f’(2) = f(2.25) – f(2) / 0.25 = 182.21 – 102 / 0.25
= 320.84
Єt = 283 – 320.8 / 283 = -13.36%
Now calculate backward divided difference:
Xi-1 = xi –h = 2 – 0.25 = 1.75
F(xi-1)= f(1.8) = 25 . (1.8)3 -6 (1.8)2 + 7 (1.8) – 88
= 50.96
F’(2) = f(2) – f(1.8) / 0.25 = 102 – 50.96 / 0.25 = 204.16
Єt = 283 – 204.16 / 283 = 27.86%
Finally, centered divided difference is obtain by inserting f(xi+1) and f (xi-1):
F’(2) = f(2.25) – f(1.8) /2 x 0.25 = 320.84 -50.96 / 0.5 = 539.68
Єt = 283 – 539.68 / 283 = -90.7%
