Exercises for Question Type 1: Finding the tangent and normal to a polynomial at a specific value of x

Question 1

Skill question

Find the equation of the tangent line to the curve $y = 6 x^{3} - x + 1$ at $x = - 1$ .

[5]

Question 2

Skill question

Find the equation of the tangent line to the curve $y = 7 x^{4} + 5 x^{2} - x + 4$ at $x = - 2$ .

[6]

Question 3

Skill question

Find the equation of the tangent line to the curve $y = 3 x^{3} + 6$ at $x = 2$ .

[5]

Question 4

Skill question

Find the equation of the tangent line to the curve $y = 4 x^{2} - x + 7$ at $x = - 2$ .

[5]

Question 5

Skill question

Find the equation of the tangent line to the curve $y = 2 x^{3} - 3 x^{2} + x - 4$ at $x = 0$ .

[5]

Question 6

Skill question

Find the equation of the tangent line to the curve $y = 2 x^{5} - x^{4} + 3 x^{3} - x + 5$ at $x = 1$ .

[5]

Question 7

Skill question

Find the equation of the tangent line to the curve $y = 4 x^{2} + 9 x + 2$ at $x = 3$ .

[5]

Question 8

Skill question

Find the equation of the tangent line to the curve $y = 3 x^{2} + 2 x - 5$ at $x = 1$ .

[5]

Question 9

Skill question

Find the equation of the tangent line to the curve $y = 5 x^{3} + 8 x^{2} + 9 x + 3$ at $x = 5$ . [6 marks]

Find the equation of the tangent line to the curve $y = 5 x^{3} + 8 x^{2} + 9 x + 3$ at $x = 5$ .

[6]

Question 10

Skill question

Find the equation of the tangent line to the curve $y = x^{5} - 3 x^{3} + 2 x$ at $x = 2$ .

[6]

Question 11

Skill question

(No specification provided)

Find the equation of the tangent line to the curve $y = x^{4} - 2 x^{2} + 3$ at $x = 1$ .

[5]

Question 12

Skill question

Find the equation of the tangent line to the curve $y = - x^{3} + 4 x^{2} + x - 2$ at $x = 2$ .

[5]

IB Mathematics Analysis and Approaches Question Type 1: Finding the Tangent and Normal to a Polynomial at a Specific Value of x Exercises