Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 102: 1

$f’(3) = 30$

$f(x) = 5x^{2}$ $f’(3) = \lim\limits_{h \to 0} \frac{f(3+h)-f(3)}{h} = \lim\limits_{h \to 0} \frac{45 + 30h +5h^2-(5\times9)}{h}$ $f’(3) = \lim\limits_{h \to 0} \frac{45 + 30h +5h^2-45}{h}$ $f’(3) = \lim\limits_{h \to 0} \frac{30h +5h^2}{h}$ $f’(3) = \lim\limits_{h \to 0}{30 +5h}$ $f’(3) = 30 $