Solving an intial value problem using relative extrema

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Homework Help Overview

The discussion revolves around solving an initial value problem related to relative extrema, specifically focusing on the behavior of derivatives and critical points.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of first and second derivatives to analyze the problem, with some questioning whether to use limits or derivatives directly. There is a focus on understanding the significance of the first derivative at local extrema and how to apply it to find numerical values.

Discussion Status

Some participants have provided guidance on the relationship between critical points and the first derivative, noting that the derivative equals zero at local extremes. There is an ongoing exploration of how to proceed with the calculations and the implications of the results obtained so far.

Contextual Notes

Participants are working with specific values and derivatives, but there is mention of a need for clarity on the problem statement and the equations involved, which are referenced but not detailed in the thread.

DODGEVIPER13
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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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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
 
ok so should I scap my work or just plug .8 into the first derivative of what I did?
 
Answer my question, please. What is the numerical value of the first derivative of any function at a local extreme?

ehild
 
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?
 
ok so by setting y'=0 and solving for y I get -1.34909.
 
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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