E- LESSON PLAN (SUBJECT MATHEMATICS) CLASS 10+2
Lesson Plan, Class XII Subject Mathematics, chapter 6, Applications of Derivatives , for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class. E lesson planning for mathematics.
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Board – CBSE
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CLASS –XII
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SUBJECT- MATHEMATICS
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CHAPTER 6 :- Application of
derivative
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TOPIC:- Chapter : 6 : Applications of derivatives
DURATION:-
This chapter
is divided into 11 modules and is completed in 25 class meetings.
PRE-
REQUISITE KNOWLEDGE:-
TEACHING
AIDS:-
Green Board,
Chalk, Duster, Charts, smart board,
projector, laptop etc.
METHODOLOGY:- Lecture method
OBJECTIVES:-
- Rate of change of bodies.
- Increasing and decreasing functions.
- Use of derivatives in approximation.
- Maxima and minima using first and second derivative
test.
- Word problems which involves maxima and minima.
PROCEDURE
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Start the
session by asking the questions related to the trigonometry, inverse trigonometry
and formulas of derivatives. Now introduce the topic application of derivatives
step by step as follows.
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S. No.
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For Complete Explanation of Topic 
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1
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Introduction:
First of all teacher will give Introduction of the application of derivatives
in different fields of mathematics like engineering, science and social
science etc.
Now teacher will explain the term rate of change of bodies with different
examples and application of this concept in word problems.
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2
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Increasing and Decreasing of Functions
Now teacher will explain the Concept of increasing and decreasing and
their graphical representation. Also teacher will help the students in
finding the interval in which the given function is increasing or decreasing
with the help of Baby Curve Method.
a) f is strictly increasing in (a, b) if f '(x) > 0 for each x ϵ (a, b)
b)f is strictly decreasing in (a, b) if f '(x) < 0 for each x ϵ (a, b)
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3
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Slope and Tangent of a line or curve
First of all teacher will explain the term slope of a line and explain
different methods of finding the slopes of lines or curves. Teacher will also
explain the method of finding slope of tangent and equation of tangent by
taking some examples.
Slope of a line:
It is the tangent of the angle made by the line with the positive direction
of x - axis measured anti-clockwise direction. Slope of any line or curve can
be find by finding dy / dx
Equation of Tangent
Equation of the tangent at (x1, y1) is given by
y – y1 = m(x - x1) where m is the slope of the tangent
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4
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Slope and Normal of a line or curve
Here teacher will explain the Method of finding the slope of normal and
equation of normal. Also explain the relationship between slope of tangent
and normal.
Equation of Normal
Equation of the Normal at (x1, y1) is given by
y – y1 = m(x - x1) where m is the slope of the normal
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5
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Method of Approximation
Teacher will explain the method of approximation, approximate change in
surface area and volumes and approximate error. Explain the implementation of
the formula used in the method of approximation in different problems.
f(x + Δx) = f(x) + f '(x) x Δx
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6
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Maximum Value and Minimum Value
First of all teacher will provide the definition of maxima and minima and
then explain the definition by giving examples. Teacher will explain the
concept of maxima and minima graphically and geometrically so that a clear
picture will developed in the mind of the students.
Definition of Maximum Value:
Let f(x) be a real function defined on an interval I. Then f(x) is said to
have the maximum value in I, if there exist a point c in I such that f(x) ≤
f(c) for all x ϵ I
In this case f(c) is called the maximum value
Definition of Minimum Value :
Let f(x) be a real function defined on an interval I. Then f(x) is said to
have the maximum value in I, if there exist a point c in I such that f(x) ≥
f(c) for all x ϵ I
In this case f(c) is called the minimum value
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7
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Critical Points
Now explain the concept of Critical points, local maxima and local minima and
its geometrical meaning and different methods of finding local maxima and
local minima as given below.
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8
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Explain the Method of finding maxima and
minima by using first derivative test.
Algorithms used in First Derivative Test
i) Put y = f(x)
ii) Find dy/dx and put dy/dx = 0 to find the critical points.
iii) Place all the critical points on the horizontal line and write signs (
+ve or -ve) as in baby curve method.
iv) The critical point at which dy/dx changes its sign from positive to
negative is called the point of local maximum and the function have maximum
value at this point.
v) The critical point at which dy/dx changes its sign from negative (- ve) to
positive (+ ve) is called the point of local minimum and the function have
local minimum value at this point.
vi) The critical point at which dy/dx does not change its sign is called the
point of inflexion.
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9
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Explain the Method of finding maxima and
minima by using second derivative test.
Algorithms used in second derivative test
i) Put y = f(x)
ii) Find f '(x) and put f '(x) = 0 to find the critical points.
iii) Find f ''(x) and find the value of f''(x) at the critical points.
iv) If f ''(c) < 0 , then f(x) has local maximum value at x = c
v) If f ''(c) > 0, then f(x) has local minimum value at x = c
vi) If f '' (c) = 0 then test fail.
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10
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Now explain the concept of Absolute maximum
value and absolute minimum value and the method of finding these.
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11
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Explain the Implementations of Concept of
maxima and minima in daily life word problems.
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EXPECTED
OUTCOMES:-
- After
studying this lesson students should know the
- Concept rate of change of
quantities,
- Method of finding slopes of tangent and normal,
- Method of finding
the equations of slopes and tangent,
- Method of finding the approximate value of a number.
- Students
should be able to find the maximum and minimum value of the function by using
first and second derivative test.
STUDENTS
DELIVERABLES:-
- Review questions given by the teacher.
- Students should prepare the presentation in groups on different topics like
rate of change of quantities, tangents and normals, increasing, decreasing , maxima and minima of a function.
- Solve
NCERT problems with examples.
EXTENDED LEARNING:-
ASSESSMENT
TECHNIQUES:-
Assignment sheet will be given as home work at the end of the topic.
Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments.. can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.
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