Science:Math Exam Resources/Courses/MATH104/December 2013/Question 02 (b)/Solution 1

Setting the second derivative's numerator to zero yields $8(3x^{2}+4)=0$ which does not have a solution. Setting the denominator to zero yields $(x^{2}-4)^{3}=0$ which has the zeros $x=\pm 2.$ Hence $f''(x)$ is never zeros and $f''(x)$ does not exist for $x\pm 2.$