Question 1

The tangent to a curve at a point has gradient 5. Find the gradient of the normal there.

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Question 2

For the curve y = x² − 2x, find where the tangent has gradient 0 and state the equation of that tangent.

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Question 3

Find the equations of the horizontal tangents to y = x³ − 3x².

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Question 4

The tangent to y = x² − 5x is parallel to the line y = 3x + 2. Find its point of contact.

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Question 5

A curve is y = 2x² − x + 3.

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Question 6

Find the equation of the tangent to y = x² + 1 at the point where x = 2.

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Question 7

Find the equation of the tangent to y = x³ − 4x at the point where x = 1.

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Question 8

Find the equation of the normal to y = x² − 2x at the point where x = 3.

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Question 9

Find the equation of the normal to y = x³ at the point where x = 1.

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Question 10

A curve is y = x² + 1.

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Question 11

Find the equation of the normal to y = x² − 6x + 10 at its vertex.

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Question 12

Find the equation of the normal to y = 2x² − 3 at the point where x = 1.

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Question 13

The normal to y = x² at a point P has gradient 1/2. Find the coordinates of P.

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Question 14

Find the equation of the tangent to y = 4/x at the point where x = 2.

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Question 15

Find the equation of the tangent to y = √x at the point where x = 9.

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Question 16

Find the equation of the normal to y = x² − x + 1 at the point where it crosses the y-axis.

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Topic 5.4: Tangents and Normals Questions

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