October 26th, 2012, 10:47 AM  #1 
Senior Member Joined: Mar 2012 Posts: 111 Thanks: 0  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! 
October 28th, 2012, 06:58 PM  #2 
Senior Member Joined: Mar 2012 Posts: 111 Thanks: 0  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): 
October 28th, 2012, 07:20 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: maximum rate of energy consumption
You need to find P(0) right?

October 28th, 2012, 08:12 PM  #4 
Senior Member Joined: Mar 2012 Posts: 111 Thanks: 0  Re: maximum rate of energy consumption
I believe so since the starting point is at noon.

October 28th, 2012, 08:24 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  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. 
October 29th, 2012, 08:27 AM  #6 
Senior Member Joined: Mar 2012 Posts: 111 Thanks: 0  Re: maximum rate of energy consumption
ok got it, thanks Mark!


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