Equation for Tangent Line at (2,2) on f(x)=xy+y^3=12

[1MileCrash]

Homework Statement

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

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

Homework Equations

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

 

[Dick]

Homework Statement

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

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

Homework Equations

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

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

 

[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)?

 

[Dick]

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)?

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

 

[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..

 

[Dick]

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

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

(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.

 

[1MileCrash]

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

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

 

[Dick]

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

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

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.

 

[1MileCrash]

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.

Sorry about that, but thanks for the help!

 

[Dick]

Sorry about that, but thanks for the help!

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