Optimization & Stationary Points Quiz

• There are no stationary points.

• This cannot be determined without further calculation.

• Plot the function

• Integrate the function

Which of the following is a necessary condition for a point to be a local maximum or minimum?

• The first derivative is 0.

• The second derivative is 0.

• The function passes through the origin.

• The function is continuous.

What does the second derivative test tell us about a function at a stationary point?

• Whether the function is increasing or decreasing at that point.

• Whether the stationary point is a point of inflection.

• Whether the stationary point is a maximum, minimum, or point of inflection.

• The exact value of the function at that point.

If a function's first derivative is positive before a stationary point and negative after, what type of stationary point is it?

• Maximum

• Minimum

• Point of inflection

• Cannot be determined

• 1

• 2

• 3

• 0

What is the significance of a stationary point where the second derivative is zero?

• It is definitely a point of inflection.

• It is definitely a maximum.

• It is definitely a minimum.

• Further investigation is needed to determine its nature.