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NVAMediumJEE 2023Applications of Derivatives (Monotonicity, Extrema)

JEE Mathematics 2023 Question with Solution

Let the quadratic curve passing through the point (−1,0)(-1, 0) and touching the line y=xy = x at (1,1)(1, 1) be y=f(x)y = f(x). Then the x-intercept of the normal to the curve at the point (α,α+1)(\alpha, \alpha + 1) in the first quadrant is:

Answer

Correct answer:7

Step-by-step solution

Standard Method

Given: The solution states: "The correct option is (A): 77".

Find: The x-intercept of the normal.

From the provided solution, the extracted final result is 77.

Therefore, the x-intercept of the normal is 77.

Common mistakes

  • Assuming the answer key must be used even when the solution gives a different result. Here, the solution is the primary source, so the extracted answer should follow the solution result instead.

  • Confusing the point (α,α+1)(\alpha, \alpha + 1) with an arbitrary point on the curve without first using the curve conditions. The curve must satisfy both passing through (−1,0)(-1,0) and touching y=xy=x at (1,1)(1,1).

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