i don't know how or what to starts

Question

Find the slope of the tangent line to the curve 4x^2+3xy+3y^3=-251 at the point (-4,-5)

Answer 1

sure you know where to start. slope means get a derivative. In this case, use implicit differentiation to get

8x + 3y + 3xy' + 9y^2*y' = 0
y'(3x+9y^2) = -(8x+3y)

y' = -(8x+3y)/(3x+9y^2)

y' at (-4,-5) = 47/213 (?? wak!! ??)