An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 7:00 A.M.will have assembled $f ( x ) = - x ^ { 3 } + 7 x ^ { 2 } - 3 x$ transistor radios x hours later.Approximately how many radios will the worker assemble between 9:00 and 9:30 A.M.?
A)Approximately 7 radios
B)Approximately 13 radios
C)Approximately 14 radios
D)Approximately 390 radios

Question

Quizplus · Accepted Answer

To find the number of radios assembled between 9:00 and 9:30 A.M., calculate the difference in $f(x)$ at $x = 2$ (9:00 A.M.) and $x = 2.5$ (9:30 A.M.). $f(2) = -2^3 + 7(2)^2 - 3(2) = 14$ and $f(2.5) = -(2.5)^3 + 7(2.5)^2 - 3(2.5) \approx 21$. The difference is approximately 7 radios.

An Efficiency Study of the Morning Shift at a Certain f(x)=−x3+7x2−3xf ( x ) = - x ^ { 3 } + 7 x ^ { 2 } - 3 xf(x)=−x3+7x2−3x

An Efficiency Study of the Morning Shift at a Certain $f ( x ) = - x ^ { 3 } + 7 x ^ { 2 } - 3 x$