Question

What is the equation of the line tangent to the curve 2x^2-y^4 = 1 at the point (-1,1)?

Answer 1

use implicit differentiation to find slope at that point.
then calculate the tangent using that point.

Answer 2

y=mx-mPx+Py ; given m=f'(Px) and the point (Px,Py)

Answer 3

2x^2-y^4 = 1

\[ \frac{d}{dx}(2x^2-y^4) = d(1)/dx\]
\[ => 4x - 4y^3 dy/dx = 0 \]
\[ => dy/dx = x/y^3 = -1\]

or slope = -1,

If you know single point formula or slope intercept form then you will be able to find slope.