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Find the slope of the curve

  • Thread starter carlarae
  • Start date
  • #1
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Homework Statement


At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested. x^6y^6=64, normal at (2,1)


Homework Equations





The Attempt at a Solution


64/y^6
or 6x6y=0, that's as far as I am getting, totally lost.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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You know the slope of the tangent at a point is the deriverative of the curve at that point right? So you need to find the deriverave of:

[tex]
x^6 y^6 = 64
[/tex]
at (x,y)=(2,1) and (guessing - you check) y is a function of x.

you can solve the equation for y, then find y' or find the implicit deriverative:
example

[tex]\frac{dy}{dx}:x^2y^2=4[/tex][tex]
\frac{d}{dx} \left ( x^2y^2=4 \right )[/tex][tex]
y^2\frac{d}{dx}x^2 + x^2\frac{d}{dx}y^2 = 0[/tex][tex]
2xy^2 + 2yx^2\frac{dy}{dx} = 0[/tex][tex]
\frac{dy}{dx} = \frac{-2xy^2}{2yx^2} = -xy[/tex]
 

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