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Lesson: Second Derivative Test for Local Extrema

All local maximums and minimums on a function's graph are called local extrema. They occur at critical points of the function where the derivative is zero or undefined. In this lesson, we will learn how to find the local extrema using the second derivative test.

Worksheet: Second Derivative Test for Local Extrema • 14 Questions

Q1:

Determine the local maximum and local minimum values of .

Alocal maximum value 8 at , local minimum value 8 at
Blocal maximum value 8 at , local minimum value 8 at
Clocal maximum value 3 at , local minimum value at
Dlocal maximum value at , local minimum value 3 at
Elocal maximum value at , local minimum value at

Q2:

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

AThe function does not have local maximum or minimum points.
Bis a local minimum point.
Cis a local maximum point.
Dis a local maximum point.
Eis a local minimum point.

Q3:

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 minimum point, and the function does not have a local maximum point.
Cis the local maximum point, and is the local minimum 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.

Q4:

Find where (if at all) the function has its local maxima and minima.

Alocal minimum at , local maximum at
Blocal maximum at , local minimum at
Clocal minimum at , no local maximum
Dlocal maximum at , local minimum at

Q5:

Find the local maxima/minima of the function .

AThe function does not have local maximum or minimum points.
B is a local maximum point.
C is a local minimum point.
D is a local minimum point.
E is a local maximum point.

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