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5.6 Determining Concavity of Functions over Their Domains

Syllabus
2020
Topic
5.6
Level
—

Learning objectives

—FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.6• FUN-4.A Justify conclusions about the behavior of a function based on the behavior of its derivatives.• FUN-4.A.4 The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval.• FUN-4.A.5 The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity.• FUN-4.A.6 The second derivative of a function may be used to locate points of inflection for the graph of the original function.• 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 5.6

  • FUN-4.A Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  • FUN-4.A.4 The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval.
  • FUN-4.A.5 The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity.
  • FUN-4.A.6 The second derivative of a function may be used to locate points of inflection for the graph of the original function.
  • Enduring understanding FUN-4: A function’s derivative can be used to understand some behaviors of the function.