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 July 23rd, 2018, 04:06 AM #1 Member   Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 37 Thanks: 3 Can someone solve this problem? this is not a homework.
 July 23rd, 2018, 05:10 AM #2 Member   Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 37 Thanks: 3 did i solve for A) correctly?
July 23rd, 2018, 07:12 AM   #3
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Quote:
 Originally Posted by 1ucid did i solve for A) correctly?
not quite ...

note $\displaystyle \int_2^3 f(t) \, dt = -0.5$

for part (b), note $g'(x) = f(x)$

look for the intervals where $g'(x) > 0$

 July 23rd, 2018, 08:04 AM #4 Member   Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 37 Thanks: 3 Are you saying that function g(x) is not increasing for interval 2 < x < 3? Last edited by skipjack; July 23rd, 2018 at 11:18 AM.
July 23rd, 2018, 09:26 AM   #5
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Quote:
 Originally Posted by 1ucid Are you saying that function g(x) is not increasing for interval 2 < x < 3?
That is correct ...

note on $2 < x < 3$, $g'(x) = f(x) < 0 \implies g(x)$ is decreasing.

Last edited by skipjack; July 23rd, 2018 at 11:18 AM.

 July 23rd, 2018, 09:40 AM #6 Member   Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 37 Thanks: 3 But at that interval for higher value of $x$ we get higher value of $f(x)$, but never mind. Can you just do for D) please? That would be great. Last edited by skipjack; July 23rd, 2018 at 10:32 AM.
July 23rd, 2018, 10:47 AM   #7
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Quote:
 Originally Posted by 1ucid But at that interval for higher value of $x$ we get higher value of $f(x)$, but never mind. Can you just do for D) please? That would be great.
Do you see that $g'(x) = f(x)$? If so then you can compute $h'(2)$ using the product rule:
$h'(2) = 2f(2) + g(2)$

 July 23rd, 2018, 11:23 AM #8 Global Moderator   Joined: Dec 2006 Posts: 19,700 Thanks: 1804 What are your answers for (B) and (C), 1ucid?
 July 23rd, 2018, 11:29 AM #9 Member   Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 37 Thanks: 3 is this ok?
July 23rd, 2018, 11:41 AM   #10
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Quote:
 Originally Posted by skipjack What are your answers for (B) and (C), 1ucid?
This is for (B), but for (C) I'm not sure what is the right answer.

Last edited by skipjack; July 23rd, 2018 at 12:06 PM.

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