Differentiation problem and finding maximum, ing ?

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SUMMARY

This discussion focuses on solving differentiation problems to find the maximum values of three specific functions: f(x) = x² / 4 + 4 / x, f(x) = xe^(-2x²), and f(x) = sqrt(x - n) / x where n > 0. Participants emphasize the importance of demonstrating an approach to finding minima and maxima before receiving assistance. The conversation highlights the necessity of understanding differentiation techniques to tackle these types of mathematical problems effectively.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically differentiation.
  • Familiarity with finding critical points of functions.
  • Knowledge of exponential functions and their properties.
  • Ability to work with square roots and rational functions.
NEXT STEPS
  • Study techniques for finding critical points using first and second derivative tests.
  • Learn how to apply the product rule and chain rule in differentiation.
  • Explore the concept of limits and their role in determining function behavior at boundaries.
  • Practice solving optimization problems involving exponential and rational functions.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to improve their skills in solving optimization problems using differentiation.

JakePearson
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Differentiation problem and finding maximum, need helping :)?

have a few problems with these questions, can you help :)

Using differentiation, find the MAXIMUM value of the following functions?

1. f(x) = x2 / 4 + 4 / x
2. f(x) = xe-2x2
3. f(x) = sqrt(x - n) / x ; n>0

hope you guys can help !
 
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JakePearson said:
have a few problems with these questions, can you help :)

Using differentiation, find the MAXIMUM value of the following functions?

1. f(x) = x2 / 4 + 4 / x
2. f(x) = xe-2x2
3. f(x) = sqrt(x - n) / x ; n>0

hope you guys can help !

We can help, but only after you show us how you would approach them. How do you find the min and max of functions?
 

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