Features of Polynomial Functions

x = 5

Infinity

There is no Relative Maximum.

2.5 and it occurs at x = 5

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

positive nowhere and negative (-1, -4)

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

positive (-∞,∞) and negative (-4,∞)

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

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

increasing (-∞,∞) and decreasing nowhere

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

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,-∞)

(-3, 3)

(-∞, -3) U (3, ∞)

(-∞, -3] U [3, ∞)

[-3, 3]

(-∞, 2) U (-2, ∞)

(-2, 2) U (-2, ∞)

(-∞, -2) U (0.5, ∞)

(0, 2) U (0.5, ∞)

-3<x<3

-2.5<x<2.5

x>2.5

x>3

Absolute Maximum

Absolute Minimum

Relative Maximum

Relative Minimum

 $3.9$  only

 $5$  only

 $-3.3$  and  $-2.5$  

 $5$  and  $3.9$  

No Relative Maxima