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Hypochondriac
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Question:
Find the co ords of the turning points of y^3 + 3xy^2 - x^3 = 3
Attempt:
(differentiate w.r.t. x)
d/dx(y^3 + 3xy^2 - x^3) = d3/dx
3y^2(dy/dx) + 3(2xy(dy/dx) + y^2) - 3x^2 = 0
(divide through by 3)
y^2(dy/dx) + 2xy(dy/dx) = x^2 - y^2
(take dy/dx as a comon factor)
dy/dx(y^2 + 2xy) = x^2 - y^2
dy/dx = (x^2 - y^2)/(y^2 + 2xy)
now to find turning points, you set dy/dx = 0
but with explicit differentiation, there's only one variable, but there's 2 here, so I am stuck :/
Find the co ords of the turning points of y^3 + 3xy^2 - x^3 = 3
Attempt:
(differentiate w.r.t. x)
d/dx(y^3 + 3xy^2 - x^3) = d3/dx
3y^2(dy/dx) + 3(2xy(dy/dx) + y^2) - 3x^2 = 0
(divide through by 3)
y^2(dy/dx) + 2xy(dy/dx) = x^2 - y^2
(take dy/dx as a comon factor)
dy/dx(y^2 + 2xy) = x^2 - y^2
dy/dx = (x^2 - y^2)/(y^2 + 2xy)
now to find turning points, you set dy/dx = 0
but with explicit differentiation, there's only one variable, but there's 2 here, so I am stuck :/
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