Application of Derivatives

Class 12 · Mathematics

54 questions18 easy25 medium11 hard

Sample Questions

Q1.The slope of the normal to the curve y = f(x) at a point where f'(x₀) ≠ 0 is:

  • Af'(x₀)
  • B–f'(x₀)
  • C1/f'(x₀)
  • D–1/f'(x₀)

Q2.Which of the following functions is NOT monotonically increasing on R?

  • Af(x) = eˣ
  • Bf(x) = x³ + 3x
  • Cf(x) = log x (x > 0)
  • Df(x) = x³ – 3x

Q3.A critical point of f(x) is where:

  • Af(x) = 0
  • Bf'(x) = 0 or f'(x) does not exist
  • Cf''(x) = 0
  • Df'(x) is maximum

Q4.The minimum value of f(x) = x + 1/x for x > 0 is:

  • A0
  • B1
  • C2
  • De

Q5.The function f(x) = log x – x has a maximum at:

  • Ax = 0
  • Bx = e
  • Cx = 1
  • Dx = 1/e

Q6.This is a sample question to preview what you'll get in the full practice test...

  • A. Option one
  • B. Option two
  • C. Option three
  • D. Option four
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Concepts Covered

Absolute maxima and minimaApproximations using derivativesFirst derivative testIncreasing and decreasing functionsMarginal cost and revenueMaxima and minimaOptimization problemsRate of change of quantitiesSecond derivative testTangents and normals

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