Calculus Critical Numbers, Relative and Absolute Extrema

Use the diagram to classify relative and absolute extrema.

Select ALL that apply.

• A is an absolute minimum

• B is a relative maximum

• C is an absolute minimum

• D is an relative minimum

• E is an relative minimum

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 the critical number of f(x) = 4x² – 8x + 1

• x = 2

• x = 0

• x = 8

• x = 1

Find all the critical numbers of

f(x) = x³ – 6x² + 10.

Select ALL that apply

• x = 4

• x = 6

• x = -2

• x = 0

Find all the critical numbers of

f(x) = 2x³ – 6x² + 12

Select ALL that apply.

• x= 4

• x= 0

• x= -2

• x= 2

 $f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$  

Find all the critical numbers of  f(x) above
Select ALL that apply.

• x= -10

• x= 20

• x= -8

• x= -2

 $f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$  
Find the critical numbers of f(x).   Select ALL that apply

• x=2

• x=0

• x= -4

• x= -2

Find all the critical numbers of

f(x) = 6x⁴ – 16x³ – 180x² + 456.

Select ALL that apply

• x= -3

• x= 5

• x= 0

• x = 7

• x = 1

Find all the critical numbers of f(x).

 $f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13$  
Select ALL that apply.

• x= 7

• x= 5

• x= 0

• x = -2

• x = 14

Given $\left(0\le x\le2\pi\right)$  Find ALL the critical numbers in      $f\left(x\right)=6\sin x-3\sqrt{2}x$ .    Select ALL that apply     

•  $x=\frac{7\pi}{4}$  

•  $x=\frac{3\pi}{4}$  

•  $x=\frac{\pi}{4}$  

•  $x=\frac{5\pi}{4}$  

•  $x=\pi$