Science:Math Exam Resources/Courses/MATH104/December 2011/Question 02 (a)/Statement

Consider the function

$f(x)={\frac {x^{3}+x^{2}-2x-3}{x^{2}-3}}.$

Its first and second derivatives are given by

$f'(x)={\frac {(x^{2}-1)(x^{2}-6)}{(x^{2}-3)^{2}}},\qquad f''(x)={\frac {2x(x^{2}+9)}{(x^{2}-3)^{3}}}.$

Find all $x$ such that $f'(x)=0$ or $f'(x)$ does not exist.