Question

Find the slope of the curve y³ - xy² = 4 at the point where y = -1.

Answer 1

(-1)³ - x(-1)² = 4

-1 - x = 4

-x = 5

x = -5

y³ - xy² = 4

3y²(dy/dx) - (x(2y)(dy/dx) + y²(1)) = 0

3y²(dy/dx) - 2xy(dy/dx) - y² = 0

(3y - 2x)(dy/dx) = y

dy/dx = y/(3y - 2x)

= -1/(3(-1) - 2(-5))

= -1/(-3 + 10)

= -1/7