An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M.will have assembled $f ( x ) = - x ^ { 3 } + 5 x ^ { 2 } + 16 x$ transistor radios x hours later.How many radios will such a worker assemble between 10:00 and 11:00 A.M.?
A)18
B)20
C)22
D)15

Question

Quizplus · Accepted Answer

To find the number of radios assembled between 10:00 and 11:00 A.M., we calculate the difference in the number of radios assembled by 11:00 A.M. and by 10:00 A.M. Since the worker starts at 8:00 A.M., x=2 corresponds to 10:00 A.M. and x=3 corresponds to 11:00 A.M. Thus, we calculate $f(3) - f(2)$.$f(3) = -(3)^3 + 5(3)^2 + 16(3) = -27 + 45 + 48 = 66$$f(2) = -(2)^3 + 5(2)^2 + 16(2) = -8 + 20 + 32 = 44$Therefore, the number of radios assembled between 10:00 and 11:00 A.M. is $66 - 44 = 22$.

An Efficiency Study of the Morning Shift at a Certain f(x)=−x3+5x2+16xf ( x ) = - x ^ { 3 } + 5 x ^ { 2 } + 16 xf(x)=−x3+5x2+16x

An Efficiency Study of the Morning Shift at a Certain $f ( x ) = - x ^ { 3 } + 5 x ^ { 2 } + 16 x$