Find direction of tangent line to equation

[ArcanaNoir]

Homework Statement

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

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 $4x^3i+4y^3j$?

and then at the given point we would have $32i-32j$

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.

 

[SammyS]

Homework Statement

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

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 $4x^3i+4y^3j$?

and then at the given point we would have $32i-32j$

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. $32\hat{i}-32\hat{j},,$ is the direction of greatest slope. The tangent line is perpendicular to this.

 

[ArcanaNoir]

darn. so how do I find the perpendicular to that?

 

[SammyS]

darn. so how do I find the perpendicular to that?

Rotate the vector 90°.

 

[jedishrfu]

Remember doing lines perpendicular to a line how did you figure out the slope?

Negative inverse right?