For which value of x horizontal Tangent Line

[chaosblack]

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?)

 

[Shooting Star]

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.)

 

[chaosblack]

okay thanks, so the answer would just be the derivative set equal to 0?

 

[happyg1]

yes it is

 

[chaosblack]

okay thanks a lot