The point on the curve 3y = 6x − 5x³ at which the normal is parallel to the line x − 3y = 0 is:

The point on the curve 3y = 6x − 5x³ at which the normal is parallel to the line x − 3y = 0 is:

• A. (1, 1/3)
• B. (−1, −1/3)
• C. (0, 0)
• D. (2, −8/3)

Answer: A) (1, 1/3)

Explanation: y = 2x − (5/3)x³, dy/dx = 2 − 5x². The normal ∥ x − 3y = 0 (slope 1/3) ⇒ tangent slope = −3 ⇒ 2 − 5x² = −3 ⇒ x = 1, y = 1/3. Point: (1, 1/3).