


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 
Use
of differential to approximate the value of a function 
Rules
for differentials 
Differentials
of some basic functions 
Higher order derivatives and higher order differentials 
Higher order derivatives 
Higher order derivatives examples 
Higher derivative formula for the product  Leibniz formula 
Higher derivatives of composite functions 
Higher derivatives of composite functions examples 
Higher derivatives of implicit functions 
Higher derivatives of implicit functions examples 
Higher derivatives of parametric functions 
Higher derivatives of parametric functions examples 
Higher order differentials 
Higher order differentials examples 
Applications
of differentiation  the graph of a function and its derivative 
Definition
of increasing and decreasing 
Increasing/decreasing
test 
Rolle's theorem

The mean value theorem 
Generalization
of the mean value theorem

Cauchy's mean value theorem or generalized mean value theorem 
L'Hospital's
rule  limits of indeterminate forms 
Applications
of L'Hospital's
rule  evaluation of limits of indeterminate forms, examples 
a)
Applications
of differentiation  the graph of a function and its derivatives 
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 NewtonRaphson method) 
Use of
Newton's method example 
b)
Applications
of differentiation  the graph of a function and its derivatives 
Taylor's
theorem (Taylor's
formula)  The extended mean value theorem 
The proof of Thaylor's theorem 
Maclaurin's
formula or Maclaurin's theorem 
Representing
polynomial using Maclaurin's and Taylor's formula 
Representing
polynomial using Maclaurin's and Taylor's formula examples 
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 















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