The equation x^2 y+2xy^3=8defines y as a function of x,y=f(x), near x=2, y=1.

Question

a) Find dy/dx.

b) Now, find the slope of the curve
x^2y+2xy^3=8 when x=2, y=1.

Answer 1

differentiate implicitly,

x^2 + 2xy^3 = 8
2x + 2x(3y^2)dy/dx + 2(y^3) = 0

solve for dy/dx, then for b) sub in x=2, y=1