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

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

Find all $x$ such that $f^{\prime }(x)=0$ or $f^{\prime }(x)$ does not exist.