Calc Review for Quiz 5. 2nd Sem. Absolute Extrema& Rolle's Theo

Use the diagram to classify relative and absolute extrema.

Select ALL that apply.

• (0,0) is an absolute minimum

• (1,-14) is an absolute minimum

• (4, 40) is an absolute maximum

• (6, 10) is an relative minimum

• (7, 65) is an absolute maximum

Find all the critical numbers of

f(x) = 3x⁴ – 8x³ – 90x² + 700.

Select ALL that apply

• x= -3

• x= 5

• x= 0

• x = 7

• x = 1

• Absolute minimum occurs when x = 9

• Absolute minimum occurs when x = 2

• Absolute minimum occurs when x = 5

• Absolute maximum occurs when x = 5

• Absolute maximum occurs when x = 9

• 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

• 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

Find the two x - intercepts of  f(x) = x² + 4x - 77,  and then find x that verifies  Rolle’s Theorem within the intercept.

• x is -2 located between the intercepts (-7, 11)

• x is -2 located between the intercepts (-11, 7)

• x is -4 located between the intercepts (-11, 7)

• x is 2 located between the intercepts (-7, 11)

• Yes and c=2

• Yes and c=3/8 or 0.375

• Yes and c=-12

• No

• No

• Yes and c= -3/2

• Yes and c=-1/2

• Yes and c=-5/2

• Yes and c=1.875 (15/8)

• Yes and c=3.75 (15/4)

• No, there is none.

• Yes and c=0