Extreme Value Theorem

What is the absolute min of this function?

• 0
• -7.5
• -7.5 and 0
• 4

Tags

CCSS.HSA.REI.D.10

For each problem, find all points of absolute minima and maxima.

• A

• B

• C

• D

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

In order for the Extreme Value theorem to apply, which of these must be true. Select all that apply.

• It must be a function

• It must be closed

• It must be open

• It must be continuous

• It must be discontinuous

Find the absolute extrema of

g(x) = 3x³ + 6x² on [-1, 1].

• abs max value of 9 when x = 1, abs min value of 3 when x = -1

• abs max value of 9 when x = 1, abs min value of 0 when x = 0

• abs max value of 9 when x = 1, abs min of -1 when x = -1

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

Which of the following is the absolute maximum value of the function y = x³ –3x² -1 on the given interval [-1, 4]?

• -1

• 5

• 15

• 49

Tags

CCSS.HSA.APR.B.3

Find the absolute extrema of

f(x) = 3x³ – 18x² + 20 on the closed interval [ -1, 7].

Select ALL the correct answers. (Feel Free to use Desmos Graphing Tool)

• Absolute maximum occurs when x = 7

• Absolute minimum occurs when x = -1

• Absolute maximum occurs when x = 4

• Absolute minimum occurs when x = 4

• Absolute minimum occurs when x = 0

• Absolute minimum occurs when x = -7

• Absolute maximum occurs when x = -2

• Absolute minimum occurs when x = -2

• Absolute maximum occurs when x = 6

• Absolute minimum occurs when x = 4

• x = 0

• There are no critical numbers for f(x) on this interval.

Tags

CCSS.HSF-IF.C.7D

Find the absolute min and max.

• 
• 
• 
• 

Tags

CCSS.HSA.REI.D.10