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Calculus

Tangents and Normals

jee_main_2026_april_2_shift_1

Grade 12

Question:

The equation of the tangent to the curve y = x^2 at x = 1 is:

A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Step-by-Step Solution

Key Concept: Equation of tangent: y - y1 = m(x - x1).

Step 1: y = x^2, dy/dx = 2x. At x = 1, m = 2. Step 2: Point (1, 1). Tangent: y - 1 = 2(x - 1) => y = 2x - 1.

Correct Answer: A

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