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