Question

Find points at which the tangent to the curve y = x³ − 3x² − 9x + 7 is parallel to the x-axis.

Answer 1

When x = 3, y = (3)³ − 3 (3)² − 9 (3) + 7 = 27 − 27 − 27 + 7 = −20.

When x = −1, y = (−1)³ − 3 (−1)² − 9 (−1) + 7 = −1 − 3 + 9 + 7 = 12.

Hence, the points at which the tangent is parallel to the x-axis are (3, −20) and

(−1, 12).