Application of Derivatives

This topic covers concepts such as Application of Derivative, Average Rate of Change of a Function, Instantaneous Rate of Change of a Function, Derivative as (Instantaneous) Rate of Change of a Function, Approximations in Calculus, etc.

This topic covers concepts such as Tangents and Normals, Geometrical Meaning of Derivative of a Function, Tangent to a Curve, Slopes of Tangent at a Point on a Curve y=f(x), Length of Tangent to a Curve, Subtangent to a Curve, etc.

This topic covers concepts such as Interaction between Two Curves, Intersection of Two Curves, Angle of Intersection of Two Curves, Orthogonal Intersection of Two Curves, Two Curves Touches Each Other, Equation of Common Tangents to Two Curves, etc.

This topic covers concepts such as Monotonicity of a Function, Monotonically Increasing/Decreasing Function in an Interval, Strictly Increasing/Decreasing Function in an Interval, Test for Increasing and Decreasing Function in an Interval, etc.

This topic covers concepts such as Mean Value Theorems, Rolle's Theorem, Geometrical Explanation of Rolle's Theorem, Algebraic Interpretation of Rolle's Theorem, Lagrange's Mean Value Theorem (LMVT), Solving Inequalities Using LMVT, etc.

This topic covers concepts such as Maxima and Minima of a Function, Existence of Maxima and Minima of a Function in an Interval, Global Maximum and Minimum of a Function, Local Maximum and Minimum of a Function, Maxima, etc.