# Approximating slope of the derivative at a point

1. Nov 29, 2007

### demersal

1. The problem statement, all variables and given/known data
The slope of the line tangent to the curve y^3 + x^2y^2 - 3x^3 = 9 at (1.5,2) is approximately

2. Relevant equations
A) 0.39
B) 3.2
C) -11.45
D) -2.29
E) -3.2

3. The attempt at a solution
Well, I solved for the derivative, but I'm not sure if it was to any avail seeing as when I plug the point back in I do not get an answer choice.

I got:

dy/dx = (-2xy^(2) + 9x^2) / (3y + 2x^(2)y)

Did I solve the derivative incorrectly? Or is plugging in the point not the correct course of action? Thank you again for all your help, I've been struggling with this problem a lot and any guidance/explanation would be great!

2. Nov 29, 2007

### dotman

Hello,

It looks like you made a small error in your implicit differentiation-- go back and double check, see if you can spot it.

Hope this helps.

3. Dec 1, 2007

### amolv06

Yep, I think you simply dropped an exponent on the y from the denominator. I got

$$\frac{dy}{dx}=\frac{9x^{2}-2xy^{2}}{3y^{2}+2x^{2}y}$$

Plugging in the numbers, I get .393. Hope that helps.

Last edited: Dec 1, 2007