If it is an astroid, then it should be
x^(2/3) +y^(2/3) =4
the way you typed it would result in a circle
http://www.wolframalpha.com/input/?i=x%5E2%2F3+%2By%5E2%2F3+%3D4
(2/3)x^(-1/3) + (2/3)y^(-1/3) dy/dx = 0
x^(-1/3) + y^(-1/3) dy/dx = 0
dy/dx = -(x^(-1/3))/y^(-1/3)
= -(x/y)^(-1/3)
= -(y/x)^(1/3)
at the point (-3√3 , 1)
dy/dx = -(2/(-3√3))^(1/3)
equation of tangent:
y-1 = -(2/(-3√3))^(1/3)(x + 3√3)
simplify if you have to
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 +y^2/3 =4
(-3sqrt(3),1)
(astroid)
1 answer
1 answer