Question

Find the slope of the tangent line to the graph of x= 5y^3-6y ^2 - 3 at (-4,1)

Answer 1

implicit differentiation

take derivitive of both sides

1=15y^2dy/dx-12ydy/dx
1=dy/dx(15y^2-12y)
divide both sides by (15y^2-12y)
1/(15y^2-12y)=dy/dx

sub the point (-4,1)
1/(15(1)^2-12(1))=dy/dx
1/(15-12)=dy/dx
1/3=dy/dx
slope is 1/3