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Lesson: Local Extrema and Critical Points

All local maxima and minima 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 local extreme values using the first derivative theorem.

Worksheet: Local Extrema and Critical Points • 22 Questions

Q1:

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 maximum point.
Cis a local minimum point.
Dis a local minimum point.
Eis a local maximum point.

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 the local maximum and minimum values of .

Alocal maximum 4 at , local minimum 40 at
Blocal maximum at , local minimum at
Clocal maximum 28 at , local minimum at
Dlocal maximum at , local minimum 28 at
Elocal maximum at , local minimum at

Q4:

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

Q5:

Determine, if any, the local maximum and minimum values of , together with where they occur.

AThe local maximum is at , and there is no local minimum.
BThe local maximum is at , and the local minimum is at .
CThe local minimum is at , and there is no local maximum.
DThe local minimum is at , and the local maximum is at .

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