Chapter 3 - The Derivative - 3.4 Definition of the Derivative - 3.4 Exercises - Page 176: 15

$f'(x)=\frac{-12}{x^{2}}$ $ f'(-2) = -3$ $ f'(0)=0$ $f'(3)=\frac{-4}{3}$

$f(x+h)=\frac{12}{x+h}$ $f(x+h) - f(x) =\frac{12}{x+h} - \frac{12}{x}=\frac{12x-12x -12h}{x(x+h)}=\frac{-12h}{x(x+h)}$ $\frac{f(x+h) - f(x)}{h}=\frac{\frac{-12h}{x(x+h)}}{h}=\frac{-12}{x(x+h)}$ $f'(x) = \lim\limits_{h \to 0} \frac{-12}{x(x+h)} =\frac{-12}{x(x+0)}=\frac{-12}{x^{2}}$ $ f'(-2) = -3$ $ f'(0)=0$ $f'(3)=\frac{-4}{3}$