Learn.

Step 1

Identify your turning points in your function – these will become the x intercepts of your derivative function.

As seen below, the turning point is when the tangent to the function is parallel to the x axis.

Step 2

Identify your inflexion points in your function – these will become the turning points of your derivative function.

As seen below, the inflexion point is when the function changes from concave up to concave down or vice versa.

Step 3

Identify your horizontal inflexion points in your function – these will become the turning points and x intercepts of your derivative function.

As seen below, the horizontal inflexion point is when the function changes from concave up to concave down or vice versa as well as the tangent at that point being parallel to the x axis.

Master.

Question 1. [2 marks]

Sketch the derivative of the following function.

Question 2.

Sketch the derivative of the following function. [3 marks]

Answers.

Question 1.

Question 2.