Exercises for Question Type 1: Finding intervals where a function is increasing or decreasing

Question 1

Skill question

Determine the intervals of increase and decrease for $f (x) = \frac{x}{x ^{2} + 1}$ .

[7]

Question 2

Skill question

Determine intervals of increase/decrease for $f (x) = x e^{- x}$ on $[0, \infty)$ .

[6]

Question 3

Skill question

Find the intervals of increase and decrease for $f (x) = x^{4} - 4 x^{3} + 4 x^{2}$ .

[6]

Question 4

Skill question

Determine where $f (x) = 3 x^{3} - 9 x + 2$ is increasing or decreasing.

Question 5

Skill question

Determine the intervals of increase and decrease for $f (x) = cos x$ on $[0, 2 π]$ .

[4]

Question 6

Skill question

For $f (x) = sin x$ on $[0, 2 π]$ , find the intervals where $f$ is increasing or decreasing.

[4]

Question 7

Skill question

Determine the intervals on which $f (x) = x^{3} - 5 x^{2} + 6 x + 9$ is increasing and decreasing.

[5]

Question 8

Skill question

Find the intervals where $f (x) = \frac{1}{( x - 1 ) ^{2}}$ is increasing and decreasing for $x \in R, x \neq = 1$ .

[5]

Question 9

Skill question

Find where $f (x) = ln x - x$ is increasing and decreasing for $x > 0$ .

[4]

Question 10

Skill question

Find the intervals of increase and decrease for $f (x) = x^{4} - 2 x^{2} + 1$ .

[5]

Question 11

Skill question

Find the intervals on which the function $f (x) = x^{3} + x^{2} - x + 5$ is increasing or decreasing.

[5]

Question 12

Skill question

Determine intervals of increase and decrease for $f (x) = x ln x$ on $(0, \infty)$ .

[6]

IB Mathematics Analysis and Approaches Question Type 1: Finding Intervals Where a Function Is Increasing or Decreasing Exercises