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Implicit Differentiation; Tangent Line

  • Thread starter b521
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  • #1
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Homework Statement


Find the equation of a tangent line at the curve at point (-3√3, 1)

x^(1/3) + y^(1/3) = 4


Homework Equations


Point-slope:
y-1=m(x-1)

The Attempt at a Solution



I took the derivative of that equation and resulted in
-y^(2/3)/x^(2/3)

When I tried plugging in x and y to get slope, the equation got very messy and I couldn't get a number out of it. Can anyone help me out?
 
Last edited:

Answers and Replies

  • #2
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Homework Statement


Find the equation of a tangent line at the curve at point (-3√3, 1)

x^(1/3) = y^(1/3) = 4
Looks like there is a typo here.

Homework Equations


Point-slope:
y-1=m(x-1)
This would be the line with slope m, that passes through (1, 1).

The Attempt at a Solution



I took the derivative of that equation and resulted in
y^(2/3)/x^(2/3)
It's hard to tell whether this is correct, since the original equation likely has a typo. If you typed '=' in place of '+', then you have a sign error in your derivative. Also, it would be helpful to have an equation for your derivative; e.g., y' = y^(2/3)/x^(2/3).
When I tried plugging in x and y to get slope, the equation got very messy and I couldn't get a number out of it. Can anyone help me out?
 
  • #3
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Here's all of my work:

(1/3)x^(-2/3) + 1/3y^(-2/3)(dy/dx) = 0

(dy/dx)1/3y^(2/3) = -1/3x^(2/3)
dy/dx = -3y^(2/3)/3x^(2/3)
dy/dx = -y^(2/3)/x^(2/3)

I hope that helps find my problem. This is where I tried plugging in the x value and everything got complicated.

1/(-3√3)^(2/3)
 
  • #4
33,627
5,284
What is the original equation? I can't tell if your work is correct without knowing the original equation.
 
  • #5
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(-3√3)^(2/3) can also be written as ((-3√3)^2)^(1/3)
 
  • #6
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What is the original equation? I can't tell if your work is correct without knowing the original equation.
x^(1/3) + y^(1/3) = 4

This is the original equation. Sorry about the typo before.
 
  • #7
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That's what I thought, but I wanted to make sure. You should have enough information to complete the problem now.
 
  • #8
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(-3√3)^(2/3) can also be written as ((-3√3)^2)^(1/3)
Just to make sure, the slope is 1/3?
 
  • #9
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I get -1/3.
 

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