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Lesson: First Derivative Test for Local Extrema

Worksheet: First Derivative Test for Local Extrema • 25 Questions

Q1:

The graph of the first derivative of a continuous function is shown. At what values of does have a local maximum and a local minimum?

  • A has local maximum points at and and a local minimum point at .
  • B has local maximum points at and and local minimum points at and .
  • C has a local maximum point at and local minimum points at and .
  • D has local maximum points at and and local minimum points at and .
  • E has local maximum points at and and a local minimum point at .

Q2:

The graph of the first derivative of a continuous function is shown. At what values of does have a local maximum and/or a local minimum?

  • A has a local maximum point at and local minimum points at and .
  • B has a local maximum point at .
  • C has local maximum points at and and local minimum points at and .
  • D has a local minimum point at .
  • E has local maximum points at and and local minimum points at and .

Q3:

The graph of the derivative of a function is shown. At what values of does have a local maximum or minimum?

  • A has a local maximum at and a local minimum at .
  • B has a local maximum at and and local minimums at and .
  • C has a local maximum at , and , a local minimum at and .
  • D has a local maximum at and and local minimums at and .
  • E has a local maximum at and local minimums at and .

Q4:

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.

Q5:

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
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