An efficiency study of the morning shift at certain factory indicated that an average workers we who arrives on the job at (:00 AM will have assembled f(x)= -2x^3+12x^2+15x transistor radios x hours later.
a) Derive a formula for the rate at which the worker will be assembling radios after x hours.
b) At what rate will the worker be assembling radios at 10:00 a.m.?
c) How many radios will the workers actually assemble between 10:00 am.m and 11:00 a.m.?
Thank you soooo much!
f(x)=-2x^3+12x^2+15x?
2011-11-27 10:48 pm
回答 (2)
2011-11-27 11:12 pm
I'm assuming (:00 AM means 9:00 AM.
a) The rate will just be the first derivative of the original function, or
f'(x) = -6x^2 + 24x + 15.
b) At 10:00 AM one hour has passed so plug in 1 for f'(x): -6(1) + 24(1) + 15 = 33 radios per hour.
c) To find this just take f(2) - f(1), f(2) being the number of radios assembled by 11:00 and f(1) being the number of radios assembled by 10:00. -2(8) + 12(4) + 15(2) - (-2(1) + 12(1) + 15) = -16 + 48 + 30 + 2 - 12 - 15 = 37 radios.
a) The rate will just be the first derivative of the original function, or
f'(x) = -6x^2 + 24x + 15.
b) At 10:00 AM one hour has passed so plug in 1 for f'(x): -6(1) + 24(1) + 15 = 33 radios per hour.
c) To find this just take f(2) - f(1), f(2) being the number of radios assembled by 11:00 and f(1) being the number of radios assembled by 10:00. -2(8) + 12(4) + 15(2) - (-2(1) + 12(1) + 15) = -16 + 48 + 30 + 2 - 12 - 15 = 37 radios.
2011-11-27 10:49 pm
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