1) Find the slope of the tangent line to the curve: 2xy + 4y^3 = -570 at point(7, -5)
2) Fin the slope of the tangent line to the curve: 2((x^2)+(y^2))^2 = 25((x^2)-(y^2)) at point (3,1)
2) Fin the slope of the tangent line to the curve: 2((x^2)+(y^2))^2 = 25((x^2)-(y^2)) at point (3,1)
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1) You have to use implicit differentiation:
2xy' + 2y + 12y^2 * y' = 0
y'[2x + 12y^2] = -2y
y' = -2y / [2x + 12y^2]
Now plug in (7,-5):
y' = -2(-5) / [2(7) + 12(-5)^2]
= 10/[14 + 300
= 10/314
= 5/157
2xy' + 2y + 12y^2 * y' = 0
y'[2x + 12y^2] = -2y
y' = -2y / [2x + 12y^2]
Now plug in (7,-5):
y' = -2(-5) / [2(7) + 12(-5)^2]
= 10/[14 + 300
= 10/314
= 5/157