Extrema

5-5 The Absolute Extrema

Guided Notes

Multiple Select

Use the diagram to classify relative and absolute extrema.

Select ALL that apply.

• A is an absolute maximum

• B is a relative maximum

• C is an relative maximum

• D is an absolute minimum

• E is an relative minimum

Multiple Select

Find all the critical numbers of

f(x) = 2x³ – 6x² + 12

Select ALL that apply.

• x= 4

• x= 0

• x= -2

• x= 2

Multiple Select

Find the absolute extrema of   $$f\left(x\right)=-5x+3$$  on the closed interval        [ -2, 4].   Select ALL the correct answers.  

• Absolute maximum occurs when x = 4

• Absolute maximum occurs when x = -2

• Absolute minimum occurs when x = -2

• Absolute minimum occurs when x = 4

• Absolute maximum occurs when x = 5

Multiple Select

Find the absolute extrema of   $$f\left(x\right)=x^3-3x^2-24x+4$$  on the closed 

interval [ -4, 8].   Select ALL the correct answers.  

• Absolute minimum occurs when x = -4

• Absolute maximum occur when x = -2

• Absolute minimum occurs when x = 4

• Absolute maximum occurs when x = 4

• Absolute maximum occurs when x = 8

Multiple Select

Find the absolute extrema of   $$f\left(x\right)=4x^2-24x+6$$  on the closed interval [ 0, 8].   Select ALL the correct answers. 

• Absolute minimum occurs when x = 0

• Absolute maximum occurs when x = 3

• Absolute minimum occurs when x = 3

• Absolute maximum occurs when x = 8

• Absolute minimum occurs when x = 8