Equation of a tangent

CalculusCourse skill

Use a point and the derivative to find the tangent line.

At , the point is and the tangent gradient is .
Use .
Simplify the equation. A zero tangent gradient gives a horizontal line.

Example 1

Find an equation of the tangent to the curve at .

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Example 2

Find an equation of the tangent to the curve at .

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Your turn

5 practice questions

Question 1

Find an equation of the tangent to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Question 2

Find an equation of the tangent to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Question 3

Find an equation of the tangent to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Question 4

Find an equation of the tangent to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Question 5

Find an equation of the tangent to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Use the point-gradient form.

Example 1

Example 2

Your turn

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