Solve the problem.Let Q(x) = bo + b1(x - a) + b2(x - a)2 be a quadratic approximation to f(x) at x = a with the properties:i. Q(a) = f(a)ii. Q '(a) = f '(a)iii. Q "(a) = f "(a)(a) Find the quadratic approximation to f(x) = at x = 0.(b) Do you expect the quadratic approximation to be more or less accurate than the linearization? Give reasons for your answer.

Question

What will be an ideal response?

Answer 1

(a) Q(x) =  -  + 
(b) I expect the quadratic approximation to be more accurate than the linearization. The linearization accounts for how the value of f(x) is changing at the point x = a, but the quadratic approximation also accounts for the change in this change by incorporating the second derivative into the approximation.