Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 115: 15

$s'(t) = 3t^{2} -2t$ and $ s'(-1) =5$

Consider $s(t) = t^{3} - t^{2} \implies s(-1) = -1-1 = -2$ Now, $s'(t) = 3t^{3-1} -(2)t^{2-1} \implies s'(t) = 3t^{2} -2t$ and $ s'(-1) = 3(-1)^{2} -2(-1)=5$ Hence. $s'(t) = 3t^{2} -2t$ and $ s'(-1) =5$