Exercises for Question Type 2: Calculating the normal to the curve at the point where tangent is known

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Exercises for Question Type 2: Calculating the normal to the curve at the point where tangent is known - IB

Question 1

Calculate the equation of the normal to the curve y = x^{2} + 2 x + 1 at the point where the tangent is parallel to the line y = 4 x + 3 .

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Question 2

For the curve y = 3 x^{3} - x, find the equations of the normals at the points where the tangent is horizontal.

[5]

Question 3

Calculus

Find the equation of the normal to y = 4 x^{4} - 8 x^{2} + 5 at x = 1 .

[5]

Question 4

Calculus: Differentiation and Tangents/Normals.

The normal to the curve y = x^{2} + k x + 3 at x = 3 has gradient - \frac{1}{4} . Find the value of k and the equation of this normal.

[6]

Question 5

Finding the equation of a normal to a polynomial curve at a given point.

Find the equation of the normal to the curve y = x^{5} - 5 x + 4 at x = 2 .

[6]

Question 6

Find the equation of the normal to the curve y = x^{4} - 2 x + 1 at x = 1 .

[5]

Question 7

For the curve y = \frac{1}{x}, find the equation(s) of the normal(s) at the point(s) where the tangent is parallel to the line y = - x + 4 .

[8]

Question 8

The normal to y = x^{3} - a x^{2} + b x - 1 at x = 1 is y = x + 2 . Find the values of a and b .

[7]

Question 9

The tangent to the curve y = 2 x^{3} + x^{2} - 4 x + 1 is y = 4 x - 4 . Find the equation of the normal at the point of contact.

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Question 10

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

[3]

Question 11

Find the equations of the normals to the curve y = x^{3} - 3 x + 2 at the points where the tangents are parallel to the line y = 9 x - 7 .

[7]

Question 12

Find the equation of the normal to the curve y = 3 x^{3} - x^{2} + 2 at the point where x = - 1 .

[6]

IB Mathematics Applications & Interpretation Question Type 2: Calculating the Normal to the Curve at the Point Where Tangent Is Known Exercises