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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)
Solution
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).
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