Exercises for Question Type 1: Finding the derivative of a polynomial with different ranges of integers

Question 1

Skill question

Differentiate $f (x) = - 4 x^{4} + 7 x^{3} - x + 5$ .

[3]

Question 2

Skill question

For $f (x) = 4 x^{3} - 5 x^{2} + 6 x - 2$ , find $f^{'} (x)$ and $f^{''} (x)$ .

[4]

Question 3

Skill question

Find the derivative of the function $f (x) = 5 x^{3} + 8 x^{2} + 9 x + 3$ .

[3]

Question 4

Skill question

Determine the stationary points of $f (x) = x^{4} - 4 x^{3} + 6 x^{2}$ .

[6]

Question 5

Skill question

Find the derivative of $f (x) = 2 x^{3} - 9 x^{2} + 4 x - 7$ .

[3]

Question 6

Skill question

Given $f (x) = 7 x^{4} - x^{3} + 2 x^{2} - 5 x + 11$ , find $f^{'} (2)$ .

[4]

Question 7

Skill question

Find $f^{'} (x)$ if $f (x) = 6 x^{5} - 3 x^{2} + 12$ .

[2]

Question 8

Skill question

Find the equation of the tangent to $y = 3 x^{3} - x + 2$ at $x = 1$ .

[5]

Question 9

Skill question

Calculus: Finding inflection points of polynomial functions.

Find the coordinates of the inflection point(s) of the curve $y = x^{3} - 6 x^{2} + 9 x$ .

[4]

Question 10

Skill question

Find all values of $x$ such that the gradient of the curve $y = - 2 x^{5} + 3 x^{4} - x^{2} + x - 4$ is zero.

[4]

Question 11

Skill question

Let $f (x) = 2 x^{3} - 3 x^{2} + 4 x + 1$ . Find $f^{'} (x)$ .

[2]

Question 12

Skill question

Compute the second derivative of $f (x) = x^{5} - 5 x^{3} + 4 x$ .

[4]

IB Mathematics Applications & Interpretation Question Type 1: Finding the Derivative of a Polynomial with Different Ranges of Integers Exercises