Features of Polynomial Functions

What is the Relative Maximum of this function?

• x = 5

• Infinity

• There is no Relative Maximum.

• 2.5 and it occurs at x = 5

Identify the intervals where the function is positive and where it is negative.

• positive (-1, ∞) and negative (-∞, -1)

• positive nowhere and negative (-1, -4)

• positive (-∞,-3) and (1,∞) and negative (-3,1)

• positive (-∞,∞) and negative (-4,∞)

Identify where the function is increasing and where it is decreasing.

• increasing (-1, ∞) and decreasing (-∞,-1)

• increasing (-∞, -1) and decreasing (-1, ∞)

• increasing (-∞,∞) and decreasing nowhere

• increasing (-1, -4) and decreasing (-3, 1)

Where is the function positive and where is it negative?

• positive (-2,1) and (3,∞) and negative (-∞,-2) and (1,3)

• positive (-∞,-1) and (2,∞) and negative (-1,2)

• positive (-1,4) and negative (2,-2)

• positive (∞,3) and (1,-2) and negative (3,1) and (-2,-∞)

When is this function decreasing?

• (-3, 3)

• (-∞, -3) U (3, ∞)

• (-∞, -3] U [3, ∞)

• [-3, 3]

On which interval(s) is the given function increasing?

• (-∞, 2) U (-2, ∞)

• (-2, 2) U (-2, ∞)

• (-∞, -2) U (0.5, ∞)

• (0, 2) U (0.5, ∞)

When is this function increasing?

• -3<x<3

• -2.5<x<2.5

• x>2.5

• x>3

Where is the decreasing?

• ( −∞, −2.55) U (0, 2.55)
• (∞, −6.25) U (36, −6.25)
• ( −∞, −2.55] U [0, 2.55]
• (−∞, 0)

The blue dot on this graph represents a(n)...

• Absolute Maximum

• Absolute Minimum

• Relative Maximum

• Relative Minimum

What are the Relative Maxima of this graph?

•  $3.9$  only
  

•  $5$  only

•  $-3.3$  and  $-2.5$  
  

•  $5$  and  $3.9$  

• No Relative Maxima