# Lesson Worksheet: Second Derivative Test for Local Extrema Mathematics • Higher Education

In this worksheet, we will practice classifying local extrema using the second derivative test.

Q1:

Find, if any, the points where has a local maximum or local minimum.

• Ais a local maximum point.
• Bis a local minimum point.
• Cis a local minimum point.
• DThe function does not have local maximum or minimum points.
• Eis a local maximum point.

Q2:

Find, if any, the points where has a local maximum or local minimum.

• Ais the local minimum point, and the function does not have a local maximum point.
• Bis the local maximum point, and is the local minimum point.
• Cis the local minimum point, and the function does not have a local maximum point.
• Dis the local maximum point, and the function does not have a local minimum point.
• Eis the local minimum point, and is the local maximum point.

Q3:

Find, if any, the local maximum and local minimum values of .

• AThe function does not have local maximum or minimum points.
• BThe local maximum value is.
• CThe local maximum value is, and the local minimum value is.
• DThe local minimum value is, and the local maximum value is.
• EThe local minimum value is.

Q4:

Find the coordinates of all the local minima and maxima of the function .

• AThere are no local minima or maxima values.
• BLocal minima at and local maxima at
• CLocal minima at
• DLocal minima at
• ELocal minima at and local maxima at

Q5:

Find the local maxima/minima of the function .

• A is a local maximum point.
• B is a local minimum point.
• C is a local minimum point.
• D is a local maximum point.
• EThe function does not have local maximum or minimum points.

Q6:

Find the local maximum and minimum values of , if there are any. Round your answer to the nearest three decimal places.

• AThe local minimum value and the local maximum value .
• BThe local minimum values are 0.066 and .
• CThe local maximum values are , and .
• DThe local maximum values are 0.066 and .
• EThe local minimum value and the local maximum value .

Q7:

Find the local maximum and minimum values of , if any.

• AThe local maximum value is .
• BThe local minimum value is .
• CThe local minimum value is 0.
• DThe local maximum value is 0.
• E does not have any local maximum or minimum values.

Q8:

Find the local maximum and minimum values of , if any.

• AThe local maximum value is 2 and the local minimum value is .
• BThe local maximum value is 0.
• CThe local minimum value is 2.
• DThe local maximum value is 2.
• E does not have any local maximum or minimum values.

Q9:

Find the local maximum and minimum values of .

• Alocal minimum 0 at
• Blocal maximum 0 at
• Clocal minimum at
• Dno local maximum and no local minimum values
• Elocal maximum at

Q10:

Find the local maxima and local minima of , if any.

• Alocal minimum at , local maximum at
• Blocal minimum at , local maximum at
• Clocal minimum at , local maximum at
• Dlocal minimum at , local maximum at
• Elocal minimum at , local maximum at

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