For the given functions f (x), let x0 = 1, x1 = 1.25, and x2 = 1.6.

Question:

For the given functions f (x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f (1.4), and find the absolute error.
a. f (x) = sin πx
b. f (x) = 3√(x - 1)
c. f (x) = log10(3x − 1)
d. f (x) = e2x - x