Question

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

Answer 1

The equation of the given curve is 

Now, the tangent is parallel to the x-axis if the slope of the tangent is zero.

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).