Chapter 4 - Analyzing Change: Applications of Derivatives - 4.4 Activities - Page 281: 20

$g^{'}(t)=-3t^2+24t+36$ $g^{''}(t)=-6t+24$ Point of inflection occurs at input $t=4$

$g(t)=-t^3+12t^2+36t+45$ Taking derivative with respect to t $g^{'}(t)=-3t^2+24t+36$ Taking derivative with respect to t $g^{''}(t)=-6t+24$ Putting $-6t+24=0$ $-6t=-24$ $6t=24$ $t=\frac{24}{6}=4$ Point of inflection occurs at input $t=4$