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Lesson: Concavity and Points of Inflection

The second derivative of a function may be used to determine whether the function is concave up or concave down on any intervals in its domain. In this lesson, we will learn how to determine the concavity of the functions and inflection points from that test.

Worksheet: Concavity and Points of Inflection • 25 Questions

Q1:

Determine the intervals on which is concave up and concave down.

  • AThe function is concave up on the interval and concave down on the interval .
  • BThe function is concave up on the interval and concave down on the interval .
  • CThe function is concave up on the interval and concave down on the interval .
  • DThe function is concave up on the interval and concave down on the interval .
  • EThe function is concave up on the interval and concave down on the interval .

Q2:

Determine the intervals on which the function is concave up and down.

  • AThe function is concave up on and and concave down on and .
  • BThe function is concave up on and and concave down on and .
  • CThe function is concave up on and and concave down on and .
  • DThe function is concave up on and and concave down on and .
  • EThe function is concave up on and and concave down on and .

Q3:

Determine the intervals on which the function is concave up and down.

  • AThe function is concave down on and concave up on .
  • BThe function is concave down on and and concave up on .
  • CThe function is concave down on and concave up on .
  • DThe function is concave down on and concave up on .
  • EThe function is concave down on and concave up on .

Q4:

Determine the intervals on which is concave up and down.

  • AThe function is concave down on the interval and up on the interval .
  • BThe function is concave down on the interval and up on the interval .
  • CThe function is concave down on the interval and up on the interval .
  • DThe function is concave down on the interval and up on the interval .
  • EThe function is concave down on the interval and up on the interval .

Q5:

Determine where is concave up and/or where it is concave down.

  • AThe function is concave down on the interval .
  • BThe function is concave up on the interval .
  • CThe function is concave down on the interval .
  • DThe function is concave down on the interval .
  • EThe function is concave up on the interval .
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