12M06
Applications of Derivatives
1 2 3 4 5
5
4
3
2
1
X
Y
Time (s) ⟶
S ↑
(m)
Minimum = ??
Maximum = ??
Equation = ??
Velocity ??
12M06.1
Rate of Change of Quantities
12M06.1 - Rate of Change of Quantities
Learninig Objectives
What is Rate of Change
How to calculate Rate of Change
Finding Rate of change using Chain Rule
5
12M06.0 – Revision
6
Recall Test
12M06.1
CV 1
What is Rate of Change
f
Displacement
Independent
Dependent
12M06.1
CV 2
How to Calculate Rate of Change
Time (s) ⟶
S ↑
(m)
X
Y
1 2 3 4 5
5
4
3
2
1
Average Rate of Change
1 2 3 4 5
5
4
3
2
1
X
Y
Time (s) ⟶
S ↑
(m)
Velocity ??
Instantaneous Rate of Change
PSV 01
Given | Asked | Known |
- | | |
What is Given | What is Asked | What do we Know |
- | | |
Did you Know?
PSV 02
Given | Asked | Known |
| | |
What is Given | Asked | Know |
| | |
What is
What do we
12M06.1
CV 3
Finding Rate of change using Chain Rule
Chain Rule
PSV 03
Given | Asked | Known |
| | |
Given | Asked | Known |
| | |
PSV 04
Given | Asked | Known |
| | |
|
Given | Asked | Known |
| | |
|
ConcepTest
Ready for Challenge
Given | Asked | Known |
| | |
|
Given | Asked | Known |
| | |
|
12M06.1 – Rate of Change of Quantities
Reference Questions
NCERT : 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18
Work Book : 5, 9, 13, 16, 17
12M06.2 – Increasing and Decreasing Functions
Reference Questions
NCERT : 2, 3, 4, 6, 8, 9, 10, 11, 12, 13, 15, 17, 19
Work Book : 1, 3, 6, 10, 15
12M06.3 – Tangents and Normals
Reference Questions
NCERT : 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20,
22, 23, 25, 26
Work Book : 4, 8, 11
12M06.4 – Approximations
Reference Questions
NCERT : 1, 2, 3, 4, 7, 9
12M06.5 – Maxima and Minima
Reference Questions
NCERT : 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 28, 29
Work Book : 2, 7, 12, 14, 18, 19, 20
12M06.2
Increasing and Decreasing Functions
12M06.2 – Increasing and Decreasing Functions
Learninig Objectives
Increasing and Strictly Increasing Functions
Decreasing and Strictly Decreasing Functions
Conditions for Increasing and Decreasing Functions
50
12M06.2
CV 1
Increasing and Strictly Increasing Functions
Increasing
Increasing
Strictly
12M06.2
CV 2
Decreasing and Strictly Decreasing Functions
Decreasing
Decreasing
Strictly
Neither Increasing nor Decreasing Functions
Increasing
Decreasing
Increasing
Neither Increasing nor Decreasing Function
Increasing Functions | Strictly Increasing Functions | Decreasing Functions | Strictly Decreasing Functions | Neither Increasing nor Decreasing Functions |
| | | | |
12M06.2
CV 3
Conditions for Increasing and Decreasing Function
Mean Value Theorem
Increasing
Decreasing
Constant
Increasing
Decreasing
Constant
Strictly Increasing
Strictly Decreasing
At a Point
In an Interval
PSV 05
Taking LCM
Taking LCM
PSV 06
| |
| |
PSV 07
|
|
| |
ConcepTest
Ready for Challenge
| |
|
12M06.3
Tangents and Normals
12M06.3 – Tangents and Normals
Learninig Objectives
Finding Equation of Tangent
Finding Equation of Normal
78
Did You Know ?
Slope
Fixed Point
O
P
Tangent
Normal
Special Cases for Two Lines
Equation of a Straight Line
Perpendicular
Parallel
12M06.3
CV 1
Finding Equation of Tangent
12M06.3
CV 2
Finding Slope of Tangent
Sol.
Slope
12M06.3
CV 3
Equation of Tangent
Sol.
PSV 08
Sol.
12M06.3
CV 4
Finding Slope of Normal
Sol.
12M06.3
CV 5
Finding Equation of Normal
Equation of Tangent
Equation of Normal
Slope of Normal
Slope of Tangent
PSV 09
Sol.
Equation of normal
| |
| |
| |
PSV 10
Sol.
ConcepTest
Ready for Challenge
Pause the Video
(Time Duration : 05 minutes)
Sol.
| |
| |