Find direction of tangent line to equation

  • Thread starter ArcanaNoir
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  • #1
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Homework Statement



Find the direction of the line tangent to the curve [itex] x^4+y^4=32 [/itex] at the point [itex] (2, -2) [/itex]

Homework Equations



Anything goes, we're in vector calculus now.

The Attempt at a Solution



So, to find the tangent line, I was thinking of taking the gradient, but I'm not sure how to do that since the curve is in a squirrely format. I think they call that "implicit".

Perhaps the gradient is [itex] 4x^3i+4y^3j [/itex]?

and then at the given point we would have [itex] 32i-32j [/itex]

Is this actually the direction of the line tangent to the curve at the given point? Is this actually the answer? I don't really know.
 

Answers and Replies

  • #2
SammyS
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Homework Statement



Find the direction of the line tangent to the curve [itex] x^4+y^4=32 [/itex] at the point [itex] (2, -2) [/itex]

Homework Equations



Anything goes, we're in vector calculus now.

The Attempt at a Solution



So, to find the tangent line, I was thinking of taking the gradient, but I'm not sure how to do that since the curve is in a squirrely format. I think they call that "implicit".

Perhaps the gradient is [itex] 4x^3i+4y^3j [/itex]?

and then at the given point we would have [itex] 32i-32j [/itex]

Is this actually the direction of the line tangent to the curve at the given point? Is this actually the answer? I don't really know.
No. [itex] 32\hat{i}-32\hat{j},, [/itex] is the direction of greatest slope. The tangent line is perpendicular to this.
 
  • #3
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darn. so how do I find the perpendicular to that?
 
  • #4
SammyS
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darn. so how do I find the perpendicular to that?
Rotate the vector 90°.
 
  • #5
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Remember doing lines perpendicular to a line how did you figure out the slope?

Negative inverse right?
 

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