calc 1 homework help.

Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

y²(y² − 4) = x²(x² − 5)

(0, −2)

(devil's curve)

Answer 1

y^2 ( 2yy') + (y^2 - 4)2yy' = x^2( 2x) + (x^2-5)(2x)

(2yy')( 2y^2 - 4) = (2x) ( 2x^2 - 5)

(2yy')(y^2-2) = x(2x^2 - 5) <--- divides everything by 2

y' = x(2x^2 - 5)/((2y)(y^2-2))

the slope is m= 0 at x=0

y = -2