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Find all points on the graph of y^3−27y=x^2−90 at which the tangent line is vertical.?
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- JLv 74 years ago
2x dx = 3y^2 dy - 27dy
2x dx = (3y^2 - 27) dy
dx/dy = (3y^2 - 27) / 2x = 0 if y=3 or if y=-3
If y = 3 the given equation is 27(1-3) = x^2-90 giving x=6 or -6, that gives two points
(6,3) and (-6,3).
If y =-3 the given equation is 54 = x^2-90 giving x=12 or x=-12, which gives two more points
(12,-3) and (-12,-3)
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