estimating the value of a function using 3rd

Question

Estimating the value of a function using 3rd Taylor polynomial.

Consider the 3^rd Taylor polynomial P₃(x) for the function f(x) = √x with anchor point a = 4.

(a)Use P₃ to estimate √5, and use our error guarantee to give a Plus- or-minus error to your estimate.

(b)Using our usual error guarantee, for which values of x with x > 4 we guarantee that P₃(x) is an estimate of √x to within 10^-2?