Functions Contents - F
Differential calculus
Differential Calculus - Derivatives and differentials The derivative of a function
Tangent to a curve The equation of the line tangent to the given curve at the given point Determining the lines tangent to the graph of a function from a point outside the function
lines tangent to the graph of a function from a point outside the function example The derivative as a function Derivatives of basic or elementary functions Differentiation rules
The derivative of the sum or difference of two functions
A constant times a function rule
The quotient rule Table of derivatives of elementary functions The chain rule applications Implicit differentiation
Implicit differentiation examples Generalized power rule
Generalized power rule examples Logarithmic differentiation
Logarithmic differentiation examples Derivative of a composite exponential function
Use of the logarithmic differentiation
Derivatives of composite functions examples Derivatives of the hyperbolic functions
Derivatives of inverse hyperbolic functions Derivative of the inverse function
Derivatives of the inverse trigonometric functions Derivative of parametric functions, parametric derivatives
Derivative of parametric functions example Derivative of vector-valued functions
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
Use of differential to approximate the value of a function
Rules for differentials
Differentials of some basic functions 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    