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October 26th, 2012, 10:47 AM   #1
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maximum rate of energy consumption

totally lost here. what is the maximum value? I figured out the time (noon) but not the last part. Thanks!


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October 28th, 2012, 06:58 PM   #2
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Re: maximum rate of energy consumption

oops sorry was over the upload count for my imageshack, here's the problem I need help with (got everything else, need the last part):


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October 28th, 2012, 07:20 PM   #3
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Re: maximum rate of energy consumption

You need to find P(0) right?
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October 28th, 2012, 08:12 PM   #4
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Re: maximum rate of energy consumption

I believe so since the starting point is at noon.
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October 28th, 2012, 08:24 PM   #5
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Re: maximum rate of energy consumption

You use t = 0, not because this is noon, but because this is where the power consumption is at a maximum.





Now, equating the first derivative to 0, we find:

where



Since the period of the sinusoidal energy function is 24 hr, we need only consider

So, we look at:

i) we find so this extremum is a maximum.

ii) we find so this extremum is a minimum.

So, we find the maximum power consumption occurs at . Now evaluate the power function at this point to find the maximum power consumption.
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October 29th, 2012, 08:27 AM   #6
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Re: maximum rate of energy consumption

ok got it, thanks Mark!
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