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Calculate the Intervals of Increase and Decrease for the Following Functions:

Exercise 1

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Exercise 2

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Exercise 3

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Exercise 4

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Exercise 5

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Exercise 6

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Exercise 7

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Exercise 8

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Exercise 9

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Exercise 10

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Exercise 11

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Exercise 12

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Exercise 13

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Exercise 14

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Exercise 15

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Exercise 16

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Exercise 17

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Solution of exercise 1

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing:

$\text{[math]}$

Decreasing:

$\text{[math]}$

Solution of exercise 2

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 3

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 4

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

After solving the cubic equation, we will get:

$\text{[math]}$ {}^{}

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 5

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 6

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

No solutions in .

Decreasing: $\text{[math]}$

Solution of exercise 7

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 8

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 9

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 10

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 11

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Hence we got no solution

Increasing: $\text{[math]}$

Solution of exercise 12

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Solution of exercise 13

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 14

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Both solutions can't be solved

Decreasing: $\text{[math]}$

Solution of exercise 15

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$\text{[math]}$ is the only possible solution

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 16

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ is the only possible solution

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

Solution of exercise 17

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Increasing: $\text{[math]}$

Decreasing: $\text{[math]}$

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Chapters

Calculate the Intervals of Increase and Decrease for the Following Functions:
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6
Solution of exercise 7
Solution of exercise 8
Solution of exercise 9
Solution of exercise 10
Solution of exercise 11
Solution of exercise 12
Solution of exercise 13
Solution of exercise 14
Solution of exercise 15
Solution of exercise 16
Solution of exercise 17

Increase and Decrease Worksheet

Calculate the Intervals of Increase and Decrease for the Following Functions:

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Solution of exercise 7

Solution of exercise 8

Solution of exercise 9

Solution of exercise 10

Solution of exercise 11

Solution of exercise 12

Solution of exercise 13

Solution of exercise 14

Solution of exercise 15

Solution of exercise 16

Solution of exercise 17

Theory

Exponent Rules

Composition of Functions

Constant Functions

Convergent and Divergent Sequences

Even and Odd Functions

Exponential Function

Graphing Parabolas

Arithmetic Sequence

Mean Value Theorem

Rolle’s Theorem

Intervals of Increase and Decrease

Periodic Functions

Graphing rational function I

Graphing rational function III

Inflection Points

Increasing and Decreasing Functions

Piecewise Functions

Trigonometric Functions

Linear Function

Domain of a Function

Maxima, Minima and Inflection Points

Linear Functions Worksheet

Monotone Sequence

Radical Functions

Function

Geometric Sequence

Coordinates of X Intercept Explained: GCSE and A Level

Bounded Sequence: Monotonic and Non-Monotic

L’Hôpital’s Rule

Graphing polynomial function I

Types of Functions

Coordinates in the Plane

Optimization

nth Term

Graphing rational function V

Limit of a Sequence

Absolute Value Function

Sequences

Geometric Sequence Problems And Solutions

Arithmetic Sequence Problems with Solutions

Logarithmic Functions

Concave and Convex Functions: Theory and Examples

Rational Functions: Graphs, Hyperbolas and Asymptotes Explained