Question

Using implicit differentiation, find the slope of the tangent line to the curve -4x^2+2xy−6y^3=−576
at the point (8,4)

Answer 1

\[8x+2xy'+2y-18y^2y'=0\]

Answer 2

solve for y'

Answer 3

then replace x by 8 and y by 4

Answer 4

\[8x+2y=18y^2y'-2xy'\]
\[8x+2y=(18y^2-2x)y'\]
\[y'=\frac{8x+2y}{18y^2-2x}=\frac{4x+y}{9y^2-x}\]

Answer 5

Plugged in the values and it didn't work. Are you sure about the derivative? isn't it -8x+2xy′+2y−18y2y′=0 ?