What is the extreme f(x)=x+4/x ,0.2<= x<= 8 ?

The extreme f(x)=x+4/x ,0.2<= x<= 8 is Maximum(0.2,20.2),Minimum(2,4),Maximum(8, 17/2)

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extreme f(x)=x+4/x ,0.2<= x<= 8

extreme

Maximum (0.2, 20.2), Minimum (2, 4), Maximum (8, \frac{17}{2})

Solution steps

Find the critical points:

x = 0.2, x = 2, x = 8

Domain of

x + \frac{4}{x}, 0.2 \leq x \leq 8 : 0.2 \leq x \leq 8

Find intervals:

Decreasing

: 0.2 < x < 2,

Increasing

: 2 < x < 8

Plug the extreme point

x = 0.2

into

x + \frac{4}{x} \Rightarrow y = 20.2

Maximum (0.2, 20.2)

Plug the extreme point

x = 2

into

x + \frac{4}{x} \Rightarrow y = 4

Minimum (2, 4)

Plug the extreme point

x = 8

into

x + \frac{4}{x} \Rightarrow y = \frac{17}{2}

Maximum (8, \frac{17}{2})

Maximum (0.2, 20.2), Minimum (2, 4), Maximum (8, \frac{17}{2})

What is the extreme f(x)=x+4/x ,0.2<= x<= 8 ?
The extreme f(x)=x+4/x ,0.2<= x<= 8 is Maximum(0.2,20.2),Minimum(2,4),Maximum(8, 17/2)