CUET · MATHS · PYQ PAPER 2023
Points at which normal to the curve \(y=x^3-3 x\) is parallel to \(y\)-axis are:
- A \((1,2)\) and \((1,-2)\)
- B \((1,-2)\) and \((-1,2)\)
- C \((1,2)\) and \((-1,-2)\)
- D \((-1,2)\) and \((1,2)\)
Answer & Solution
Correct Answer
(B) \((1,-2)\) and \((-1,2)\)
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx} = 3x^2 - 3 \) \( 3x^2 - 3 = 0 \Rightarrow x^2 = 1 \Rightarrow x = \pm 1 \) For \( x = 1 \): \( y = (1)^3 - 3(1) = -2 \). Point: \((1, -2)\) For \( x = -1 \): \( y = (-1)^3 - 3(-1) = 2 \). Point: \((-1, 2)\)
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