CalculusAdditional / Further Maths

Finding stationary points

Solve for zero gradient and find the corresponding coordinates.

  • A stationary point has .
  • Differentiate, solve this equation, then substitute each solution into .
  • Give both coordinates of every stationary point.

Example 1

Find the coordinates of all stationary points.

Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.

Example 2

Find the coordinates of all stationary points.

Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.Find the corresponding ordinate.

Remember
A stationary point need not be a maximum or minimum.

Your turn

Question 1

Find the coordinates of all stationary points.

Check answer
Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.
Question 2

Find the coordinates of all stationary points.

Check answer
Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.Find the corresponding ordinate.
Question 3

Find the coordinates of all stationary points.

Check answer
Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.
Question 4

Find the coordinates of all stationary points.

Check answer
Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.Find the corresponding ordinate.
Question 5

Find the coordinates of all stationary points.

Check answer
Differentiate and factorise.A stationary point has zero gradient.Solve for the stationary values.Find the corresponding ordinate.
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