Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 102: 7

$f’(1) = 5 $

$f(x) = x^3 +2x $ $ f’(1) = \lim\limits_{h \to 0}{\frac{f(1+h) - f(1)}{h}} $ $ f’(1) = \lim\limits_{h \to 0} \frac{(1+h)^3 + 2(1+h) -(1^3+2)}{h} $ $f’(1) = \lim\limits_{h \to 0} \frac{h^3+3h^2+5h}{h} $ $f’(1) = \lim\limits_{h \to 0} h^2 +3h +5 $ $f’(1) = 5 $