Given the curve of C defined by the equation x^2 - 2xy +y^4 =4.

Question

1) Calculate the slope of the tangent line at any value of t.

2) Find the tangent line at t= (1/2)(Pi).

Answer 1

First you find dy/dx by doing doing implicit differentiation.

To find the slope at a t-value, you plug in that t-value into dy/dx.

But wait a minute, dy/dx will be in terms of x, so you can NOT plug in a value for t.

Problem can not be done.