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Lesson: Second Derivative Test for Local Extrema

In this lesson, we will learn how to find local extrema using the second derivative test.

Sample Question Videos

06:27
09:02

Worksheet • 13 Questions • 2 Videos

Q1:

Find the local maximum and minimum values of 𝑓 ( π‘₯ ) = 2 √ π‘₯ βˆ’ 4 √ π‘₯ 4 .

  • Alocal minimum βˆ’ 2 at π‘₯ = 1
  • Bno local maximum and no local minimum values
  • Clocal maximum βˆ’ 2 at π‘₯ = 1
  • Dlocal minimum 0 at π‘₯ = 1 6
  • Elocal maximum 0 at π‘₯ = 1 6

Q2:

Find, if any, the point ( π‘₯ , 𝑦 ) where 𝑦 = βˆ’ π‘₯ + 4 π‘₯ βˆ’ 6 2 has a local maximum or local minimum.

  • A ( 2 , βˆ’ 2 ) is a local maximum point.
  • BThe function does not have local maximum or minimum points.
  • C ( 2 , βˆ’ 2 ) is a local minimum point.
  • D ( βˆ’ 2 , βˆ’ 1 8 ) is a local minimum point.
  • E ( βˆ’ 2 , βˆ’ 1 8 ) is a local maximum point.

Q3:

Find, if any, the local maximum and local minimum values of 𝑓 ( π‘₯ ) = 1 9 π‘₯ + 1 5 π‘₯ s i n c o s , together with their type.

  • Aabsolute maximum = 24.21, absolute minimum = βˆ’ 2 4 . 2 1
  • Babsolute maximum = βˆ’ 2 4 . 2 1 , absolute minimum = 24.21
  • Cabsolute maximum = βˆ’ 1 9 . 7 3 , absolute minimum = 23.04
  • Dabsolute maximum = 23.04, absolute minimum = βˆ’ 1 9 . 7 3
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