Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.)

Question

x = t² − t + 9,    y = t³ − 3t

Answer 1

dy/dx = (3t² -3)/(2t -1).

For horizontal tangent dy/dx = 0; so 3t² - 3 = 0; t = ±1 and points (9, -2) and (11, 2)

For vertical tangent dy/dx undefined, so 2t - 1 = 0, t = 1/2 and point (35/4,- 11/8)