## Increasing/Decreasing intervals for Trig

Limits, differentiation, related rates, integration, trig integrals, etc.
ronny3050
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Joined: Fri Oct 12, 2012 2:51 am
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### Increasing/Decreasing intervals for Trig

Q: Let f(x)=20x-10sin(4x) for 0<=x<=pi/2
Find the largest interval(s) over which the function f is increasing or decreasing.

I tried to solve this:

f'(x)=20-40cos(4x)
=20(1-2cos(4x))

on keeping f'(x)=0, i get x=pi/12

I just cannot get correct intervals to work properly with my online math homework system!

Thank you SO much!

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Increasing/Decreasing intervals for Trig

Q: Let f(x)=20x-10sin(4x) for 0<=x<=pi/2
Find the largest interval(s) over which the function f is increasing or decreasing.

I tried to solve this:

f'(x)=20-40cos(4x)
=20(1-2cos(4x))
I think you forgot to finish: you still have to do the 4x part inside. You can see an explanation here from the Math Forum site. The Purplemath writer did something in alt groups back in 1999 here. Where PM talks about "the rest", that's the same as where MF talks about "BLOB".

ronny3050
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Joined: Fri Oct 12, 2012 2:51 am
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### Re: Increasing/Decreasing intervals for Trig

I did differentiate that! The problem is with the intervals!

Thank you!

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Increasing/Decreasing intervals for Trig

I did differentiate that!
Where? I only see the derivative for the sine, not for the 4x inside it.

ronny3050
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Joined: Fri Oct 12, 2012 2:51 am
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### Re: Increasing/Decreasing intervals for Trig

Sorry to bug you again but my function was f(x)=20x-10sin(4x)
After taking the derivative I get f'(x)=20-10*4*cos(4x) = 20-40cos(4x)

So, I did take the derivate of 4x!

Matt
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Joined: Mon May 18, 2009 3:30 pm
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### Re: Increasing/Decreasing intervals for Trig

$f(x) = 20x - 10\sin(4x)$

$f'(x)=20-40\cos(4x)=0$

$\cos(4x)=\frac12$

$4x=\pm\frac{\pi}{3}+2\pi n$

$x=\pm\frac{\pi}{12}+\frac{n\pi}{2}$

f is increasing on intervals of the form:
$[\frac{\pi}{12}+\frac{n\pi}{2},-\frac{\pi}{12}+\frac{(n+1)\pi}{2}]$

f is decreasing on intervals of the form:
$[-\frac{\pi}{12}+\frac{n\pi}{2},\frac{\pi}{12}+\frac{n\pi}{2}]$

Here's the graph of f'(x) so you can see where the derivative changes sign:
http://goo.gl/3rQCk

ronny3050
Posts: 4
Joined: Fri Oct 12, 2012 2:51 am
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### Re: Increasing/Decreasing intervals for Trig

Matt, thanks a zillion!