Extrema of Polynomials

Approximate all extrema.

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Approximate all extrema.

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What are the increasing and decreasing intervals of the graph?

• Increasing = (-∞,-3], [-1,2], [4, ∞)

  Decreasing = [-3,-1], [2,4]

• Increasing = [-3,-1], [2,4]

  Decreasing = (-∞,-3], [-1,2], [4, ∞)

• Increasing = (-∞,-3], [-1,2],

  Decreasing = [-3,-1], [2,4], [4, ∞)

• Increasing = (-∞, 2], [-3, 1], [-1, ∞)

  Decreasing = [2, -3], [1, -1]

Approximate all extrema.

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a

b

relative minimum

absolute minimum

absolute maximum

relative maximum

How many extrema (maxes and mins) are in the picture?

• 2

• 3

• 4

• 5

a

b

relative minimum

absolute minimum

absolute maximum

relative maximum

The graph of the polynomial function contains ​ (a)   absolute maximums, ​ (b)   absolute minimums, ​ (c)   local maximums, and ​ (d)   local minimums.

• 0

• 1

• 2

Label extrema

c

d

b

A relative min

A absolute max

A relative max

An absolute min

a

b

absolute minimum

absolute maximum

relative maximum

relative minimum