The curve defined by
x2/3+y2/3=42/3
is an astroid symmetric about both axes.
(a) Derive an expression for dxdy in simplest form.
(b) Determine the coordinates of every point in the first quadrant where the tangent line is horizontal. Show all steps in your reasoning and confirm that each point lies on the curve.
(c) Determine the coordinates of every point in the first quadrant where the tangent line is vertical. Show all work and verify membership on the curve.
(d) For each point found in parts (b) and (c), state the exact slope of the tangent line and explain why your values are consistent with the geometric definitions of horizontal and vertical tangents.