Application of Derivatives

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

This topic covers concepts, such as Tangent to a Curve y=f(x) From an External Point, Subnormal to a Curve, Normal to a Curve, Equations of Normal at a Point on a Curve y=f(x), Length of Subnormal, Slopes of Normal at a Point on a Curve y=f(x), etc.

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

This topic covers concepts, such as Strictly Increasing/Decreasing Function in an Interval, Test for Increasing and Decreasing Function about a Point, Concavity of a Function in an Interval, Monotonicity of a Function, Curve Sketching, etc.

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

This topic covers concepts, such as Critical Points for a Differentiable Function, Application of Maxima and Minima in Problems of Geometry, Critical Points for a Discontinuous Function, Local Maximum and Minimum of a Function, etc.