Quotient Derivative and Minima Maxima

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SUMMARY

The discussion focuses on finding the quotient derivative of the function W(z) = (4z + 9) / (2 - z) and subsequently determining its minima and maxima. The quotient rule for derivatives is applied, resulting in W'(z) = 17 / (4 - 4z + z^2). Participants emphasize the importance of plotting the function to visualize critical points and suggest that questions regarding derivatives should be directed to the appropriate calculus section for better assistance.

PREREQUISITES
  • Understanding of calculus concepts, specifically the quotient rule for derivatives.
  • Familiarity with polynomial functions and their properties.
  • Ability to analyze critical points and determine maxima and minima.
  • Experience with graphing functions to visualize behavior.
NEXT STEPS
  • Learn how to apply the first and second derivative tests to find maxima and minima.
  • Study the implications of critical points on the graph of a function.
  • Explore graphing tools or software to visualize polynomial functions effectively.
  • Review advanced calculus topics, including optimization techniques for functions.
USEFUL FOR

Students studying calculus, particularly those focusing on derivatives and optimization, as well as educators seeking to enhance their teaching methods in calculus-related topics.

zak100
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Homework Statement


Find out the quotient derivative i.e. the derivative of polynomial upon polynomial and then find the minima and maxima.[/B]

##W\left(z\right)=\frac{{4z+9}}{{2-z}}##

Homework Equations



##\left( \frac{f}{g} \right)' = \frac{f'\,g - f\,g'}{g^2}##

The Attempt at a Solution


##W'\left(z\right)=\frac{{4\left({2-z}\right)-\left({4z+9}\right)\left({-1}\right)}}{{{{\left({2-z}\right)}^2}}}##
##=\frac{{17}}{{{4-4z+z^2}}}##

I have found the quotient derivative. Some body please help me how to find the minima and maxima

Zulfi.
 
Last edited by a moderator:
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How does one normally find the maxima and minima? Also, try plotting this function and see what you get.
 
Thread moved. Questions about derivatives should be posted in the Calculus section, not in the Precalculus section.
 
Hi,
I can't find the thread.

Zulfi.
 
zak100 said:
Hi,
I can't find the thread.
The full title of the section is "Calculus & Beyond Homework."
 
zak100 said:
Hi,
I can't find the thread.

Zulfi.
You replied to it, so you have found it.
 
Hi,
I received an email that I got a reply from RPinPA . His reply is in my email but not here.

Zulfi.
 

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