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Find the Intervals of Concavity and Convexity 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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Solution of exercise 1

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 2

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Concave: $\text{[math]}$

Convex: $\text{[math]}$

Solution of exercise 3

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 4

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Convex: $\text{[math]}$

Solution of exercise 5

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No solution

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 6

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 7

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No solution

Concave: $\text{[math]}$

Solution of exercise 8

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Inflection points: $\text{[math]}$ , $\text{[math]}$

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 9

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 10

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 11

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 12

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Convex: $\text{[math]}$

Concave: $\text{[math]}$

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Concavity and Convexity Worksheet

Find the Intervals of Concavity and Convexity 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

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

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

Bounded Function Examples: Theory and Practice Questions

Maxima and Minima Examples With Solutions

Asymptote Functions: Theory and Practice Problems

Absolute Maxima Explained: Master Max/Min On Intervals

Inverse Function Explained: Simple Steps for A-Level Maths

Graphs of Quadratic Equations: Practice Questions and Answers

Applying Limits in Math: Limit Laws Made Clear

Formulas

Sequence Formulas | Arithmetic, Geometric and More

Exercises