An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 8:00 A.M. will have assembled $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } - 3 x$ transistor radios x hours later. Approximately how many radios will the worker assemble between 10:00 and 10:15 A.M.?
A) Approximately 25 radios
B) Approximately 375 radios
C) Approximately 6 radios
D) Approximately 26 radios

Question

Quizplus · Accepted Answer

To find the number of radios assembled between 10:00 and 10:15 A.M., calculate the difference in $f(x)$ at $x = 2$ (10:00 A.M.) and $x = 2.25$ (10:15 A.M.). $f(2) = -2^3 + 10(2)^2 - 3(2) = 26$ and $f(2.25) = -(2.25)^3 + 10(2.25)^2 - 3(2.25) \approx 32$. The difference is approximately 6 radios.

An Efficiency Study of the Morning Shift at a Certain f(x)=−x3+10x2−3xf ( x ) = - x ^ { 3 } + 10 x ^ { 2 } - 3 xf(x)=−x3+10x2−3x

An Efficiency Study of the Morning Shift at a Certain $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } - 3 x$