Sketching the derivative from the function

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.

A maximum turning point
A minimum turning point

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.

Horizontal inflection point marked in red, concave down to concave up

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.

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