Implicit Diff: Tangent Line at (-3*31/2,1)

[Unknown9]

Homework Statement

Implicit Differentiation:Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4 at (-3*3^1/2,1)

Homework Equations

? None?

The Attempt at a Solution

2/3 * x^-1/3 + 2/3y^-1/3*y' = 0
then after a few steps of switching the sides of the variables

y' = (-2x^1/3)/ 2/3*y^-1/3

The part that I'm just confused on is putting x into the variables, especially since we're not suppose to use calculators, any help?

 

[Dick]

3*3^(1/2)=3^(3/2). Does that help you simplify the x part?

 

[Unknown9]

3*3^(1/2)=3^(3/2). Does that help you simplify the x part?

I think I got it, does the slope end up being -3*3^1/2? Otherwise I did it incorrectly :P

 

[Dick]

Yes, I think it does. It always helps to show your work when asking question like this.

 

[Unknown9]

Wait wait wait, okay, when I plug in x... how can I plug in a negative number into that...? -3^3/2 into x^- 1/3?

 

[Dick]

x^(-1/3) is one over the cube root of x. There isn't any problem with taking the cube roots of negative numbers.