Implicit Diff.

1. Apr 6, 2008

Bo_

The problem is to find the horizontal tangent lines of an equation. Here's my attempted differentiation.

y^2 = x^3 - x + 1

{dy/dx} = (3x^2 - 1)/(2y)

Correct, or no?

i'm going to need more help going forward even if that is right, I just want to make sure it is.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 6, 2008

montoyas7940

Bo, I am pretty rusty at much of this but I will try to help since the forum is so empty at the moment.

It looks like you got the differentiation correct.

3. Apr 6, 2008

deffinitely

4. Apr 6, 2008

Bo_

ok thanks, so assuming it's right, do set equal to y, then zero? In other words:

0 = (3x^2 - 1) / 2

and then quadratic formula using that^^^^? (remember I'm trying to find all slope zero tangent lines of the original equation.) If my procedural thinking is correct, then I don't think I need any more help, thanks.

5. Apr 6, 2008

RyanSchw

You have found the slope for any point of that function except where the slope is undefined or wherever the graph may cross itself. To find the slope you would simply plug in your x and y values. However as you said you want to know the horizontal tangents.

You can't just simply set the y values to zero, you need to set the whole derivative to zero and solve the numerator for horizontal tangents, the denominator for vertical tangents.

6. Apr 6, 2008

Bo_

I can see clearly now the rain is gone, thanks.