# Homework Help: Implicit Differentiation Problem (stuck at a point)

1. Feb 17, 2004

### Cod

Here is the problem:

Find the equation of the line which is tangent to the curve at the point (1,3): 8x^3y^2 + x^2y^5 + 6 = 4y^4 - 3x^4

Here is what I've done so far (I'm stuck now):

(24x^2)(y^2) + (8x^3)(2y dy/dx) + (2x)(y^5) + (x^2)(5y^4 dy/dx) = (16y^3 dy/dx) + 12x^3

Where do I go from here? Collect like terms? Any help is greatly appreciated.

2. Feb 17, 2004

### Staff: Mentor

Start plugging in numbers and solve for dy/dx.

3. Feb 17, 2004

### Cod

Re: Re: Implicit Differentiation Problem (stuck at a point)

So I just plug in a 1 where x's are and a 3 where the y's are?

Last edited: Feb 17, 2004
4. Feb 17, 2004

### Staff: Mentor

Re: Re: Re: Implicit Differentiation Problem (stuck at a point)

You got it.

5. Feb 17, 2004

### Cod

But the differentiation process isn't done. I haven't even factored out the dy/dx yet to get the derivative. I thought I plugged in the points AFTER I found the derivative...?

6. Feb 17, 2004

### Staff: Mentor

Sure it is. All you need is dy/dx at one point, not at all points.
No need to do that!
That would be the hard way. Don't do it.

I think you are confusing what you need to do here, which is find the slope at a particular point, with a much harder problem: finding dy/dx as a function of x for all x. Lot's of luck with that one.

7. Feb 17, 2004

### paul11273

Unless I am mistaken, shouldn't the last term be -12x^3 ?
You have a + there.

I figured dy/dx=-34.
That would make the equation of the tangent line y=-34x+37.

Can someone confirm this? I am rusty...

Whoops, caught an error myself...edited to add the +37 in my answer!!!

Last edited: Feb 17, 2004
8. Feb 17, 2004

### Staff: Mentor

Good catch.
No. The line had better contain the point (1,3).

9. Feb 17, 2004

### paul11273

Yeah, I have to think a little longer next time.

y=-34x+37.