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

Consider the function

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

Its first and second derivatives are given by

$f^{\prime }(x)=\frac{(x^2-1)(x^2-6)}{(x^2-3{)}^2}$

and

$f^{″}(x)=\frac{2x(x^2+9)}{(x^2-3{)}^3}$

Find the coordinates of all local maxima, local minima, and inflection points. Be sure to indicate which is which.