Find the x-coordinates of all points where the curve might

Question

1. Show that f(x) = ³√x has a vertical tangent line at (O. O) and no horizontal tangent hues anywhere.

2. Consider the curve given by: 2y³ - y² - y⁵= x⁴- 2x³ + x².

(a) Find the x-coordinates of all points where the curve might have a horizontal tangent line.

(b) Find the y-coordinates of all of the points where the curve might have a vertical tangent line.