Chapter 12 - Section 12.3 - Higher Order Derivatives: Acceleration and Concavity - Exercises - Page 901: 4

$ -\displaystyle \frac{12}{x^{4}}$

$f''(x)=\displaystyle \frac{d}{dx}\left[\frac{df}{dx}\right]=\frac{d^{2}f}{dx^{2}}$ $\displaystyle \frac{dy}{dx}=\frac{d}{dx}[-2x^{-2}]= -2(-2x^{-3})=4x^{-3}$ $\displaystyle \frac{d^{2}y}{dx^{2}}=\frac{d}{dx}[ 4x^{-3}]=4(-3x^{-4})$=$ -\displaystyle \frac{12}{x^{4}}$