Fundamental Theorem and Maxima

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SUMMARY

The discussion focuses on determining the local maxima of the function Si(x) = ∫0x (sin(t)/t) dt. The derivative of this function is found using the Fundamental Theorem of Calculus, leading to the equation sin(x)/x = 0. The critical points occur at x = nπ, where n is an integer. Participants express confusion over the application of these concepts, particularly in visualizing the number line for maxima determination.

PREREQUISITES
  • Understanding of the Fundamental Theorem of Calculus
  • Knowledge of derivatives and critical points
  • Familiarity with the sine function and its properties
  • Ability to analyze functions on a number line
NEXT STEPS
  • Study the application of the Fundamental Theorem of Calculus in detail
  • Learn how to find local maxima and minima using the first derivative test
  • Explore the properties of the sine function, particularly its zeros
  • Practice visualizing functions and their derivatives on a number line
USEFUL FOR

Students studying calculus, particularly those focusing on integration and differentiation, as well as anyone seeking to understand the behavior of oscillatory functions like sine.

flyingpig
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Homework Statement

[tex]Si(x) = \int_{0}^{x}{\frac{sin(t)}{t} dt[/tex]

At what values of x does this function have a local maximum?
2.Solutions

[PLAIN]http://img833.imageshack.us/img833/701/27444263.png

The Attempt at a Solution



So I took the derivative and applying FTC and I got sin(x)/x = 0

sin(x) = 0

[tex]x=n\pi[/tex]

Then I drew a number line and I got lost. I looked at the solutions and I was even more lost. This is due tomorrow please help
 
Last edited by a moderator:
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PF is confused too huh? lol
 

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