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

Let ${\displaystyle f(x)}$ be a differentiable function satisfying the following properties:
          ${\displaystyle f(0)=1,f'(0)=-2,f''(0)=3;}$ and
${\displaystyle f'''(x)={\frac {6-x^{2}}{9-\cos(x)}}}$

Determine with proof and approximation A to ${\displaystyle f(2)}$ with the property that the error in the approximation is at most 1.