GATE AG 2012 • Q11 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Maxima and minima of function with several independent variables

Question Statement:

The tangent line to y = f(x) at the point (x0, y0), assuming f'(x0) ≠ 0, intersects the x-axis at:

Options:

  • (A) (x0 - y0/f'(x0), 0)
  • (B) (x0 + y0/f'(x0), 0)
  • (C) (x0 - f'(x0)/y0, 0)
  • (D) (x0 + f'(x0)/y0, 0)

Official Answer Key:

A

Step-by-Step Solution & Explanation

Tangent: y - y0 = f'(x0)(x - x0). Setting y = 0: -y0 = f'(x0)(x - x0) ⟹ x = x0 - y0/f'(x0). Answer: A.

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