Chapter 4 - Applications of the Derivative - Chapter Review Exercises - Page 221: 8

$$L(t)= 16t+ 16$$

Given $$v(t)=32 t-4 t^{2}, \quad a=2$$ Since \begin{align*} v^{\prime}(t)&=32-8t \\ v^{\prime}(2)&=16 \end{align*} Then the linear approximation is given by \begin{align*} L(t)&=v^{\prime}(a)(t-a)+v(a)\\ &= 16(t-2)+ 48\\ &=16t+ 16 \end{align*}