Science:Math Exam Resources/Courses/MATH100/December 2018/Question 08/Statement

Let $f(x)$ be a differentiable function satisfying the following properties:

          $f(0)=1,f'(0)=-2,f''(0)=3;$ and 
          $f'''(x)={\frac {6-x^{2}}{9-\cos(x)}}$

Determine with proof an approximation $A$ to $f(2)$ with the property that the error in the approximation is at most $1$.