
Grace C.
asked 11/12/20Find all points on the curve x^4+x^2*y^2+y^3=5 where the tangent line is horizontal.
I found dy/dx, but stuck on what to do next. Several of my peers are also stuck on this!
1 Expert Answer
(4x ^3 + 2xy^2) dx + (3y^2 + 2yx^2) dy = 0
dy/dx= -(4x^3 + 2xy^2)/(3y^2 + 2yx^2) = -x(4x^2 + 2y^2)/(y(3y + 2x^2))
A horizontal slope occurs when dy/dx= 0 when -x(4x^2 + 2y^2) = 0. This only occurs when x = 0, as 4x^2 + 2y^2 =0 only when x = 0 and y = 0, but this is not a solution to x^4 + x^2y^2 + y^3 = 5
Note that, when x = 0, the equation becomes y^3 = 5, or y = 51/3
Thus, our solution is (0, 51/3)
Grace C.
thank you!11/12/20
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Mark M.
The second term is not correct.11/12/20