Find points at wh

It is given that the curve y = x³ – 3x² – 9x + 7

We know that the tangent is parallel to the x-axis if the slope of the tangent is zero.

Therefore, 3x² -6x-9 = 0

⇒ x² -2x-3 = 0

⇒ (x-3)(x+1) =0

⇒ x =3 and x = -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

Therefore, the points at which the tangent is parallel to the x- axis are (3, -20) and (-1, 12).