Question 12

Mathematics Basic Geometry Medium

The point on the curve \(y=6 x-x^{2}\), where the tangent is parallel to \(x\)-axis is

(A) \((0,0)\)
(B) \((2,8)\)
(C) \((6,0)\)
(D) \((3,9)\)
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Suppose the required point is \(\left(x_{1}, y_{1}\right)\) \[\] \(\frac{d y}{d x}=6-2 x\) \[\] \(6-2 x_{1}=0 \Rightarrow 2 x_{1}=6 \Rightarrow x_{1}=3\) \[\] Point must lie on the curve \[\] \(\Rightarrow y_{1}=6 x_{1}-x_{1}{ }^{2}\) \[\] Putting \(x_{1}=3, y_{1}=18-9=9\), the point is \((3,9)\). \[\] Choice (D)\[\]

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