The function f(x)=104.5x^2 - 1501.5x + 6016, models the death rate per year per 100,000 males, f(x), for men who average x hours of sleep each night. How many hours of sleep, to the nearest tenth of an hour, corresponds to the minimum death rate, to the nearest whole number?

Question

The function f(x)=104.5x^2 - 1501.5x + 6016, models the death rate per year per 100,000 males, f(x), for men who average x hours of sleep each night. How many hours of sleep, to the nearest tenth  of an hour, corresponds to the minimum death rate, to the nearest whole number?

anonymous · Answer

f'(x)=209x-1501.5; f'(x)=0 when x= 1501.5/209=7.18. So, the minimum death rate occurs with about 7 hours of sleep.

anonymous · Answer

how can we solve this without using calculus?

anonymous · Answer

The axis of symmetry of a parabola is y=-b/2a. In this case, that would be y=1501.1/209=7.2, which rounds to 7 hours.

anonymous · Answer

Aren't we looking for x here, since the question is 'how many hours of sleep'? [argh, i really don't understand the problem.:( ]

anonymous · Answer

Sorry, you're right. It should be x=-b/2a. But the answer's the same.