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📐 Mathematics  ·  Application of Derivatives  ·  JEE

If f'(x) > 0 for all x in an interval, the function f is:

Answer: Strictly increasing.

  • A Strictly decreasing
  • B Strictly increasing
  • C Constant
  • D Undefined

Correct answer: B. Strictly increasing

Explanation: A positive derivative throughout an interval means the function is strictly increasing on that interval.

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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