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

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

          $f(0)=1,f^{\prime }(0)=-2,f^{″}(0)=3;$ 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 $1$.