Derivative and horizontal tangent help

In summary, the conversation is about finding the point at which a function has a horizontal tangent line. The equation given is (8x^2)/(x^2+8) and the derivative is found using the quotient rule: (f(x)g'(x) - g(x)f'(x))/(f(x)^2). The answer is found to be 128x/(x^2+8)^2, but the coordinates for the horizontal tangent line cannot be determined.
  • #1
kings13
27
0
Derivative and horizontal tangent help!

Homework Statement



Determine the point at which the graph of the function has a horizontal tangent line.

Homework Equations

http://www.webassign.net/cgi-bin/symimage.cgi?expr=f(x) = (8 x**2)/(x**2+8)and f(x)=x/ root2x-1endroot

The Attempt at a Solution



128x/(x^2+8)^2? no idea what I am looking for really
 
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  • #2


Your link was faulty. I have no idea which function you're referring to, but generally a horizontal tangent line is found where y'=0.
 
  • #3


yup there's a 404 not found error.
 
  • #4


fixed the link but I am having trouble finding the derivative.
 
  • #5


just use the quotient rule. the derivative of g(x)/f(x) = [tex]\frac{f(x)g'(x) - g(x)f'(x)}{f(x)^2}[/tex].EDIT: I highly recommend using Wolfram Alpha if you really get stuck. It has a show steps buttons on most derivative question!
 
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  • #6


http://www4a.wolframalpha.com/Calculate/MSP/MSP93419cd13d43b6e511700000d6f885345b6b5d7?MSPStoreType=image/gif&s=44&w=296&h=42


it says that is the answer. but that's not my problem, what is the coordinates to the answer? I am not sure what I am looking for
 
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  • #7


kings13 said:
http://www4a.wolframalpha.com/Calculate/MSP/MSP93419cd13d43b6e511700000d6f885345b6b5d7?MSPStoreType=image/gif&s=44&w=296&h=42 it says that is the answer. but that's not my problem, what is the coordinates to the answer? I am not sure what I am looking for

Well, you can't really plug anything into the derivative to make it zero. So I'm thinking that there won't be horizontal tangent in that equation.
 
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FAQ: Derivative and horizontal tangent help

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of the tangent line at that point.

How do I find the derivative of a function?

To find the derivative of a function, you can use the formula f'(x) = lim(h->0) [f(x+h)-f(x)]/h, where h is a small number representing the change in x. Alternatively, you can use differentiation rules and formulas to find the derivative of more complex functions.

What is a horizontal tangent?

A horizontal tangent is a line that is tangent to a curve at a specific point and has a slope of 0. This means that the curve is neither increasing nor decreasing at that point, and the tangent line is parallel to the x-axis.

How do I determine if a function has a horizontal tangent?

A function has a horizontal tangent at a point if its derivative is equal to 0 at that point. This means that the slope of the tangent line is 0, and the function is neither increasing nor decreasing at that point.

Why is it important to understand derivatives and horizontal tangents?

Derivatives and horizontal tangents are important concepts in calculus and other areas of mathematics. They allow us to analyze the behavior of functions and determine their rates of change at specific points. They are also useful in optimization problems, where we want to find the maximum or minimum value of a function.

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