# Tangent line equation

1. Jun 28, 2011

### 1MileCrash

1. The problem statement, all variables and given/known data

Find the equation for the tangent line at (2,2)

f(x)=xy+y^3=12

2. Relevant equations

3. The attempt at a solution

I really feel like I know what I'm doing here, but the key disagrees.

My equation for the tangent slope comes out to be:

(-y)/(x+3y^2)

when solved for my (2,2), I get a slope of -1/7

Yielding an entire equation of y= -1/7x + 12/7

2. Jun 28, 2011

### Dick

Your slope looks ok. But (2,2) isn't on your tangent line. How can that be?

3. Jun 28, 2011

### 1MileCrash

If my slope is correct, but my tangent line equation is wrong, I can only assume I did something wrong in y - y = M(x-x)?

4. Jun 28, 2011

### Dick

Sure. What did you use for the fixed y and x? Remember this line is supposed to go through (2,2).

5. Jun 28, 2011

### 1MileCrash

I used y - 2 = M (x - 2), y = 2 and x = 2.

What else could I have used? I think I'm getting confused..

6. Jun 28, 2011

### Dick

(y-2)=(-1/7)*(x-2) isn't the same line as y= -1/7x + 12/7, which you said was the answer you got. That's the only thing that's confusing for me.

7. Jun 28, 2011

### 1MileCrash

Ahh, I think I see now, a sign error?

y - 2 = -1/7x + 2/7
y = -1/7x + 16/7

8. Jun 28, 2011

### Dick

Yes. Sign error. Looks ok now. If you'd post all of your work to begin with it would be easier to diagnose these things.

9. Jun 28, 2011

### 1MileCrash

Sorry about that, but thanks for the help!

10. Jun 28, 2011

### Dick

No problem. Just suggesting a way to get faster service!