CourseCourseQ BankQuestion BankDocsDocuments

5.7 Using the Second Derivative Test to Determine Extrema

Syllabus
2020
Topic
5.7
Level
—

Learning objectives

—FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.7• FUN-4.A Justify conclusions about the behavior of a function based on the behavior of its derivatives.• FUN-4.A.7 The second derivative of a function may determine whether a critical point is the location of a relative (local) maximum or minimum.• FUN-4.A.8 When a continuous function has only one critical point on an interval on its domain and the critical point corresponds to a relative (local) extremum of the function on the interval, then that critical point also corresponds to the absolute (global) extremum of the function on the interval.• Enduring understanding FUN-4: A function’s derivative can be used to understand some behaviors of the function.

FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.7

  • FUN-4.A Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  • FUN-4.A.7 The second derivative of a function may determine whether a critical point is the location of a relative (local) maximum or minimum.
  • FUN-4.A.8 When a continuous function has only one critical point on an interval on its domain and the critical point corresponds to a relative (local) extremum of the function on the interval, then that critical point also corresponds to the absolute (global) extremum of the function on the interval.
  • Enduring understanding FUN-4: A function’s derivative can be used to understand some behaviors of the function.