The best Maths tutors available

Find the Intervals of Concavity and Convexity for the Following Functions:

Exercise 1

$\text{[math]}$

Exercise 2

$\text{[math]}$

Exercise 3

$\text{[math]}$

Exercise 4

$\text{[math]}$

Exercise 5

$\text{[math]}$

Exercise 6

$\text{[math]}$

Exercise 7

$\text{[math]}$

Exercise 8

$\text{[math]}$

Exercise 9

$\text{[math]}$

Exercise 10

$\text{[math]}$

Exercise 11

$\text{[math]}$

Exercise 12

$\text{[math]}$

Solution of exercise 1

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 2

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

Concave: $\text{[math]}$

Convex: $\text{[math]}$

Solution of exercise 3

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 4

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

Convex: $\text{[math]}$

Solution of exercise 5

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

No solution

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 6

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 7

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

No solution

Concave: $\text{[math]}$

Solution of exercise 8

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

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 9

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

$\text{[math]}$ No solution

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 10

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 11

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Solution of exercise 12

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

Convex: $\text{[math]}$

Concave: $\text{[math]}$

Summarise with AI:

Did you like this article? Rate it!

4.00 (3 rating(s))

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.

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

x- and y-Intercepts

Bounded Sequence: Monotonic and Non-Monotic

L’Hôpital’s Rule

Graphing polynomial function I

Absolute and Relative Maxima and Minima

Maxima and Minima

Types of Functions

Asymptotes

Coordinates in the Plane

Optimization

nth Term

Graphing rational function V

Limit of a Sequence

Inverse Function

Quadratic Function

Absolute Value Function

Rational Functions

Sequences

Bounded Functions

Properties of Limits

Geometric Sequence Problems And Solutions

Arithmetic Sequence Problems with Solutions

Logarithmic Functions

Concave and Convex Functions: Theory and Examples

Formulas

Sequence Formulas | Arithmetic, Geometric and More

Exercises