Chapter 5.5, Problem 11E

(a)

To determine

To calculate: The change in $F\left(x\right)=-x^2+42x+240$ from $x=10$ to $x=15$.

(b)

To determine

To sketch: The derivative of the function $F\left(x\right)$ and find the area between $F^{\prime }\left(x\right)$ and x-axis from 10 to 15 using geometric formula.

(c)

To determine

To verify: The answers obtained in part (a) and part (b) are equal as it provide the assurance by the fundamental theorem of calculus.