Increasing/Decreasing intervals for Trig  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Increasing/Decreasing intervals for Trig  TOPIC_SOLVED

Postby ronny3050 on Fri Oct 12, 2012 2:57 am

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!

Please help me!

Thank you SO much!
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Re: Increasing/Decreasing intervals for Trig

Postby FWT on Fri Oct 12, 2012 4:12 pm

ronny3050 wrote: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".
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Re: Increasing/Decreasing intervals for Trig

Postby ronny3050 on Fri Oct 12, 2012 7:20 pm

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


Could you please solve it?


Thank you!
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Re: Increasing/Decreasing intervals for Trig

Postby FWT on Sat Oct 13, 2012 2:25 am

ronny3050 wrote:I did differentiate that!


Where? I only see the derivative for the sine, not for the 4x inside it.
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Re: Increasing/Decreasing intervals for Trig

Postby ronny3050 on Sat Oct 13, 2012 2:29 am

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!
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Re: Increasing/Decreasing intervals for Trig

Postby Matt on Sat Oct 13, 2012 5:02 am











f is increasing on intervals of the form:


f is decreasing on intervals of the form:


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

Postby ronny3050 on Sat Oct 13, 2012 5:29 am

Matt, thanks a zillion! :clap:
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