Question

The points at which the tangents to the curve y = x³ – 12x + 18 are parallel to x-axis are ______.

Options

• (2, –2), (–2, –34)

• (2, 34), (–2, 0)

• (0, 34), (–2, 0)

• (2, 2), (–2, 34)

Answer 1

The points at which the tangents to the curve y = x³ – 12x + 18 are parallel to x-axis are (2, 2), (–2, 34).

Explanation:

Given that y = x³ – 12x + 18

Differentiating both sides w.r.t. x, we have

⇒ `"dy"/"dx"` = 3x² – 12

Since the tangents are parallel to x-axis, then `"dy"/"dx"` = 0

∴ 3x² – 12 = 0

⇒ x = ± 2

∴ `y_(x = 2)` = (2)³ – 12(2) + 18

= 8 – 24 + 18

= 2

`y_(x = -2)` = (– 2)³ – 12 (– 2) + 18

= – 8 + 24 + 18

= 34

∴ Points are (2, 2) and (– 2, 34).