Monotonicity and Maxima-Minima of Functions
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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
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