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📐 Mathematics  ·  Application of Derivatives  ·  JEE

If the slope of the tangent at a point is m, the slope of the normal at that point is:

Answer: -1/m.

  • A m
  • B -m
  • C 1/m
  • D -1/m

Correct answer: D. -1/m

Explanation: The normal is perpendicular to the tangent, so its slope is the negative reciprocal of the tangent slope, -1/m.

Tangent and Normal at a Point on a Curve(a,b)tangent (slope=f'(a))normal (slope=-1/f'(a))Tangent and normal are always perpendicular to each other at the point of contact

The tangent at a point touches the curve with slope f'(a); the normal is the line perpendicular to the tangent at that same point, with slope -1/f'(a) - together they describe the curve's local direction and the line "straight into" the curve.

Concept context

Use derivatives to study rate of change, increasing and decreasing functions, tangents and normals, and maxima and minima, with classic optimization problems.

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