For which value of x horizontal Tangent Line

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For which value of x...horizontal Tangent Line

Homework Statement



For which value of x does f(x) = \frac{k}{ax^{2}+bx+c} have a horizontal tangent line?


Homework Equations



Quotient Rule?

F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2?


The Attempt at a Solution



Am I supposed to just sub it into a quotient rule format, making the derivative equal to 0?

So it would look like

0 = 0 - (2ax + b)/[[ax^{2}+bx+c]^{2}]? (and then simplify of course?)
 
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That's correct. But there are certain restrictions on the values of a, b, and c.

(Also, when there is only a constant in the numerator, like f(x) = k/g(x), then you can directly use f'(x) = k d/dx[1/(g(x)] = k[-g'(x)/[g(x)^2], which is nothing but the quotient rule in a lesser number of steps.)
 
okay thanks, so the answer would just be the derivative set equal to 0?
 
yes it is
 
okay thanks alot
 
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