# Quotient Derivative and Minima Maxima

• zak100
In summary, the conversation discusses finding the quotient derivative of a polynomial upon another polynomial and then finding the minima and maxima of the resulting function. The equation for the quotient derivative is given, but help is needed for finding the minima and maxima. The thread was moved to the Calculus & Beyond Homework section.
zak100

## 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:
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,

Zulfi.

zak100 said:
Hi,
The full title of the section is "Calculus & Beyond Homework."

zak100 said:
Hi,

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.

## 1. What is a quotient derivative?

A quotient derivative is a mathematical concept used to calculate the rate of change of a function that is expressed as a quotient (fraction) of two other functions. It is also known as the derivative of the quotient.

## 2. How is a quotient derivative calculated?

To calculate a quotient derivative, you must use the quotient rule, which states that the derivative of a function expressed as a quotient is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

## 3. What is the significance of finding the quotient derivative?

The quotient derivative is useful in finding the slope of a curve at a particular point, as well as determining the critical points, minima, and maxima of a function. It is also used in optimization problems and in finding the roots of a function.

## 4. What are minima and maxima in relation to quotient derivatives?

Minima and maxima refer to the lowest and highest points, respectively, on a curve. In terms of quotient derivatives, these points can be found by setting the derivative of a function equal to zero and solving for the variable. This will give you the x-coordinate of the critical point, which can then be used to determine if it is a minimum or maximum point.

## 5. Can the quotient derivative be used to find the concavity of a function?

Yes, the quotient derivative can be used to find the concavity of a function. The second derivative of a function expresses the rate of change of the function's slope, and it can be calculated using the quotient rule. If the second derivative is positive, the function is concave up, and if it is negative, the function is concave down.

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