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Let's go

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:

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Concave:

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Solution of exercise 2

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Concave:

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Convex:

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Solution of exercise 3

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Convex:

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Concave:

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Solution of exercise 4

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Convex:

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Solution of exercise 5

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No solution Convex:

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Concave:

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Solution of exercise 6

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Convex:

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Concave:

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Solution of exercise 7

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No solution Concave:

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Solution of exercise 8

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Inflection points:

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Convex:

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Concave:

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Solution of exercise 9

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No solution

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Convex:

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Concave:

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Solution of exercise 10

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Convex:

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Concave:

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Solution of exercise 11

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Convex:

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Concave:

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Solution of exercise 12

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Convex:

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Concave:

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Summarise with AI:

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

Theory

Convergent and Divergent Sequences

Intervals of Increase and Decrease

Graphing rational function III

Increasing and Decreasing Functions

Maxima, Minima and Inflection Points

Coordinates of X Intercept Explained: GCSE and A Level

Graphing polynomial function I

Arithmetic Sequence Problems with Solutions

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

Monotone Sequences: Theory and Exercises

Linear Functions Worksheet With Solutions

Bounded Sequences: A Clear Guide to Bounds and Limits

Formulas

Sequence Formulas | Arithmetic, Geometric and More

Exercises

Concavity and Convexity Worksheet

Increase and Decrease Worksheet

Applications of Derivatives Worksheet

Exponential, Logarithmic and Trigonometric Functions Worksheet

Mean Value Theorem Word Problems

Even and Odd Functions Worksheet

Absolute Value Functions Worksheet

Finding Maxima and Minima | Worksheet with Worked Solutions

X and Y Intercepts Worksheet | Exercises with Full Solutions

Finite and Infinite Sequences Worksheet: GCSE and A Level Extension

Composition of Functions Worksheet

Maximum and Minimum Word Problems Worksheet with Answers

Quadratic Function Word Problems

Finding Inverse Functions Worksheet with Answers

Domain of a Function Worksheet

year

nth Term

Leave us a comment

Kourtney Sison

August 2026

I get it somehow, there are others who are unfamiliar and I have a hard time with it but it’s okay that I get it.

Vanessa - Editorial Manager Superprof UK

September 2026

Thanks for sharing your thoughts! It’s completely normal to find some parts unfamiliar or more difficult than others. The important thing is that you’re making progress and understanding more as you practise. Keep going! 😊

Kourtney Sison

August 2026

At least I understood some of it, but there are others that I’m confused about and have a hard time understanding, but I get it.

Vanessa - Editorial Manager Superprof UK

September 2026

Thanks for sharing! It’s great that you’ve understood some of it already. Don’t worry if a few parts are still confusing — keep practising and take your time with the trickier sections. You’ll get there! 😊

Normina Mangogawan

August 2026

The lesson was a little difficult for me, especially the word problems, but the examples helped me understand it better.

Vanessa - Editorial Manager Superprof UK

September 2026

Thanks for your feedback! Word problems can definitely be tricky, so we’re glad the examples helped make the lesson clearer. Keep practising — it gets easier with time! 😊

Kourtney Sison /Normina Mangogawan

August 2026

Thankyouuu po

Summarise with AI:

Chapters

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

Domain of a Function

Maxima, Minima and Inflection Points

Radical Functions

Function

Geometric Sequence

Coordinates of X Intercept Explained: GCSE and A Level

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

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

Monotone Sequences: Theory and Exercises

Linear Functions Worksheet With Solutions

Linear Function Problems

Bounded Sequences: A Clear Guide to Bounds and Limits

Geometric Sequence Problems

Formulas

Sequence Formulas | Arithmetic, Geometric and More

Exercises