Monotonicity and Maxima-Minima of Functions

IIT-JEE · Class 12 · Mathematics

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What’s covered

  • topics
    • Monotonicity
      • increasing and strictly increasing functions
      • decreasing and strictly decreasing functions
      • nature of composite functions
      • monotonic and non-monotonic functions
    • Applications of Monotonicity
      • finding range and number of roots using monotonicity
      • proving inequalities using monotonicity
    • Concavity
      • inequalities using concavity
      • point of inflection
    • Maxima and Minima
      • identifying extrema by checking neighbourhood values
      • second derivative test
      • first derivative test
      • extrema of discontinuous and non-differentiable functions
      • global maximum and minimum
    • Applications of Extrema
      • curve tracing and analysing roots
      • optimization in plane and coordinate geometry
      • optimization in solid geometry