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📐 Mathematics  ·  Application of Derivatives  ·  JEE

The derivative dy/dx represents the ___ of a function:

Answer: rate of change.

  • A rate of change
  • B total area
  • C enclosed volume
  • D definite integral

Correct answer: A. rate of change

Explanation: The derivative measures how fast the output changes with the input - the rate of change.

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.

Read the full Application of Derivatives notes →