Differential Calculus
Calculus Contents D
Applications of the derivative Tangent, normal, subtangent and subnormal
Property of the parabola
Property of power functions
Property of the exponential function Angle between two curves
Angle between two curves examples Differential of a function
Rules for differentials
Differentials of some basic functions
Higher order derivatives and higher order differentials Higher order derivatives Higher order differentials Definition of increasing and decreasing
Increasing/decreasing test Rolle's theorem The mean value theorem L'Hospital's rule - limits of indeterminate forms Generalization of the mean value theorem, concavity of the graph of a function Concavity of the graph of a function
Concave up and concave down definition
Points of inflection
Points of inflection and concavity of the sine function
Points of inflection and concavity of the cubic polynomial Approximate solution to an equation, Newton's method (or the Newton-Raphson method) Taylor's theorem (Taylor's formula) - The extended mean value theorem
Maclaurin's formula or Maclaurin's theorem Representing polynomial using Maclaurin's and Taylor's formula The approximation of the exponential function by polynomial using Taylor's or Maclaurin's formula
Properties of the power series expansion of the exponential function The approximation of the sine function by polynomial using Taylor's or Maclaurin's formula
Properties of the power series expansion of the sine function Extreme points, local (or relative) maximum and local minimum
The first derivative test
The second derivative test and concavity Finding and classifying critical (or stationary) points
Finding extreme points
Points of inflection
Finding points of inflection
Finding and classifying critical (or stationary) points examples    