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Finding the average value given the graph of the derivative 
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#1
Jan2513, 04:20 PM

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1. The problem statement, all variables and given/known data
Since there is a graph and many things, I will post the link of my question. http://ibhl1bccalculus.wikispaces.c...rson+text).pdf Please scroll down to the last page (page 16) and my question is 6c. 2. Relevant equations g(x)=3+∫(2,x)f(t)dt 3. The attempt at a solution Here is what I attempt to do: I try to take the integral of g(x) from 2 to 6 and then divide the solution by 4 to find the average value. However, I need to do a double integration on f(t), which I haven't learn yet. I think my approach is too complicated, so is there another way to do the problem? I also think the answer key provided in the link is wrong, can anybody tell me if it is? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Jan2513, 04:56 PM

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#3
Jan2513, 05:25 PM

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#4
Jan2513, 05:51 PM

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Finding the average value given the graph of the derivative



#5
Jan2513, 06:23 PM

P: 6

The mean of g(x) between x=2 and x=6 is = 3 + mean of f(x) f(x) has negative value between 2 and 4 with area = (1/2).pi x 1^2 = pi/2 f(x) is positive between 4 and 6 and area (1/2) x 2 x 2 = 2 Total area between 2 and 6 = 2  pi/2 = 0.4292 Mean of f(x) = 0.4292/4 = 0.1073 Mean of g(x) = 3 + 0.1073 = 3.1073 < Yet, I still don't think it is right. Can you please tell if what he did is right? 


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Jan2513, 06:38 PM

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Jan2513, 08:54 PM

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Jan2513, 10:54 PM

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Jan2613, 01:17 PM

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#10
Jan2613, 02:50 PM

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