Question

supoose that x^4 +y^4=82. 1) Use the method of implicit differentiation to find dy/dx. 20 Find the equation of the tangent line at the point (x,y)= (-1,-3).

Answer 1

Since d/dx f(y) = (dy/dx)(d/dy f(y)), by differentiating the equation wrt x on both side, 4x^3 + 4y^3(dy/dx) = 0, dy/dx = -(x/y)^3.

At (-1,-3), dy/dx = -1/27
Equation of tangent: y - y1 = m(x - x1) where x1 and y1 are coordinates of a point.
y + 3 = -1/27(x + 1)