calculus
posted by fareha on .
1. Let y = f(x) be the continuous function that satisfies the equation x^45x^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

differentiate implicitly:
4x^3  10xy^2  10x^2yy' + 16y^3y' = 0
y'(16y^3  10x^2y) = 10xy^2  4x^3
y' = x(5y^2  2x^2) / y(8y^2  5x^2)

y'(2) = 2(58) / (820) = 6/12 = 1/2
Line l is (y1)/(x2) = 1/2