Exercises for Question Type 1: Finding the stationary points of specific functions by setting first derivatives to 0

Question 1

Skill question

Find the stationary points of $f (x) = e^{- x} (x^{2} - x)$ .

[6]

Question 2

Skill question

Determine the stationary points of $f (x) = \frac{x + 1}{x - 1}$ .

[5]

Question 3

Skill question

Find the stationary points of $f (x) = x^{4} e^{- x}$ .

[5]

Question 4

Skill question

Determine the stationary points of $f (x) = x^{3} e^{- 2 x}$ .

[6]

Question 5

Skill question

Determine the stationary point of $f (x) = x e^{- x}$ .

[5]

Question 6

Skill question

Find the stationary points of $f (x) = x^{2} ln (x)$ , $x > 0$ .

Question 7

Skill question

Find the stationary points of $f (x) = \frac{x ^{2} e ^{x}}{x - 1}$ .

[7]

Question 8

Skill question

Determine the stationary points of $f (x) = 2 x^{4} - 8 x^{2} + 3$ .

[5]

Question 9

Skill question

Find the stationary points of $f (x) = x^{3} - 6 x^{2} + 9 x + 1$ .

[6]

Question 10

Skill question

Determine the stationary points of $f (x) = \frac{l n ( x )}{x}$ for $x > 0$ .

Question 11

Skill question

Find the stationary points of $f (x) = x^{2} e^{x}$ .

[5]

IB Mathematics Analysis and Approaches Question Type 1: Finding the Stationary Points of Specific Functions by Setting First Derivatives to 0 Exercises