1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2.

Question

1.	Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0   and whose graph contains the points (2, 1) and (-2, -2).  Let l be the line tangent to the graph of f at x = 2.
a.	Find an expression for y’
b.	Write an equation for line l

drwls · Answer

a. Differentiate implicitly.
4x^3 -10x*y^2 -5x^2*2y*dy/dx +16y^3*dy/dx = 0
4x^3 -10x*y^2 -10 x^2*y*dy/dx +16y^3*dy/dx = 0
Plug in x = 2 and y = 1 to get dy/dx.
4 -20 -40 dy/dx +16 dy/dx = 0
-24 dy/dx = 16
dy/dx = -2/3

b. (y - 1)/(x-2) = -2/3

Check my work.