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Solving an intial value problem using relative extrema

  • #1
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Homework Statement


See uploaded file. PROBLEM 5


Homework Equations


See uploaded file


The Attempt at a Solution


I am confused on how to go about doing the rest of this I realize I can do it with the first and second derivatives but I forgot what exactly I do with that. I know the first derivative gives me a tangent line to the curve or should I use limits to do this? SEE PROBLEM 5
 

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Answers and Replies

  • #2
ehild
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I do not understand what you tried to do. The problem asks the numerical value of y at t=0.8.
What is the value of the first derivative at a local maximum or minimum? Substitute it for y' in the equation.

ehild
 
  • #3
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ok so should I scap my work or just plug .8 into the first derivative of what I did?
 
  • #4
ehild
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Answer my question, please. What is the numerical value of the first derivative of any function at a local extreme?

ehild
 
  • #5
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Ok man you got me I really am trying so at a local extreme there has to be a critical point so the value of the derivative at that point equals zero correct?
 
  • #6
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ok so by setting y'=0 and solving for y I get -1.34909.
 
  • #7
ehild
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Correct.
You can solve the differential equation, too (although it is not asked) and use this value of y at t=0.8 to get the integration constant. And then the full y(t) function is known.

ehild
 

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