Consider the equation x^2 + 2y + xy^2 = 4?

Science & Mathematics by Anonymous 2018-05-18 11:06:05

Social Science

3 answers

Consider the equation x^2 + 2y + xy^2 = 4 a) Find y' using implicit differentiation. b) Find the slope of the tangent line to the graph of y = f(x) at the point (1, 2). c) Find the equation of the tangent line in part b).

Anonymous

Point (1,2) is not on the graph !
Anonymous

a) 2x+2y'+y^2+2xyy' = 0 y'[2+2xy] = -y^2-2x y' = -(y^2+2x)/(2+2xy) b) At (1,2) y' = -6/6 = -1 c) y-2 = -(x-1) = 1-x y = 3 - x
Anonymous

a) x^2 +2y+xy^2 = 4 Take derivative with respect to x 2x + 2 dy/dx + y^2 + x (2y) dy/dx = 0 dy/dx (2+2xy) = -(2x+y^2) dy/dx = -(2x+y^2)/(2+2xy) b) x=1; y=2 dy/dx = -(2+4) /(2+2(2)) dy/dx = -6/6 = -1 c) y-2 = -1(x-1) y = -x +1 + 2 y = -x+3