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Worksheet: Concavity of a Function

Q1:

Use the given graph of to find all possible intervals on which is concave upward.

  • A is concave upward on .
  • B is concave upward on .
  • C is concave upward on .
  • D is concave upward on .
  • E is concave upward on .

Q2:

Use the given graph of to find the coordinates of the points of inflection.

  • A ,
  • B , ,
  • C
  • D , ,
  • E

Q3:

Use the given graph of to find all possible intervals on which is concave downward.

  • A is concave downward on .
  • B is concave downward on and .
  • C is concave downward on .
  • D is concave downward on and .
  • E is concave downward on .

Q4:

Use the given graph of to find the coordinates of the point of inflection.

  • A
  • B
  • C
  • D
  • E ,

Q5:

Use the given graph of to find all possible intervals on which is concave upward.

  • A is concave upward on and .
  • B is concave upward on and .
  • C is concave upward on .
  • D is concave upward on and .
  • E is concave upward on .

Q6:

Use the given graph of to find all possible intervals on which is concave downward.

  • A is concave downward on .
  • B is concave downward on .
  • C is concave downward on .
  • D is concave downward on and .
  • E is concave downward on .

Q7:

The graph of the first derivative of a continuous function is shown. On what intervals is concave upward or concave downward?

  • A is concave upward on and and concave downward on and .
  • B is concave upward on and and concave downward on , , and .
  • C is concave upward on and and concave downward on and .
  • D is concave upward on , , and and concave downward on and .
  • E is concave upward on and and concave downward on and .

Q8:

The graph of the first derivative of a continuous function is shown. On what intervals is concave upward or concave downward?

  • A is concave upward on and and concave downward on and .
  • B is concave upward on and concave downward on and .
  • C is concave upward on and and concave downward on and .
  • D is concave upward on and and concave downward on .
  • E is concave upward on , , and and concave downward on and .