What is the extreme f(x)=x+4/x+8,1<= x<= 8 ?

The extreme f(x)=x+4/x+8,1<= x<= 8 is Maximum(1,13),Minimum(2,12),Maximum(8, 33/2)

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extreme f(x)=x+4/x+8,1<= x<= 8

extreme points

f (x) = x + \frac{4}{x} + 8, 1 \leq x \leq 8

Maximum (1, 13), Minimum (2, 12), Maximum (8, \frac{33}{2})

Solution steps

Find the critical points:

x = 1, x = 2, x = 8

Domain of

x + \frac{4}{x} + 8, 1 \leq x \leq 8 : 1 \leq x \leq 8

Find intervals:

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < 8

Plug the extreme point

x = 1

into

x + \frac{4}{x} + 8 \Rightarrow y = 13

Maximum (1, 13)

Plug the extreme point

x = 2

into

x + \frac{4}{x} + 8 \Rightarrow y = 12

Minimum (2, 12)

Plug the extreme point

x = 8

into

x + \frac{4}{x} + 8 \Rightarrow y = \frac{33}{2}

Maximum (8, \frac{33}{2})

Maximum (1, 13), Minimum (2, 12), Maximum (8, \frac{33}{2})

y = 1 x e^{3 x^{2}}

f (x) = \frac{1}{x + 7}

f (x, y) = x^{2} - x y + y^{2} - 2 x + y

f (x) = 9 + 4 x^{2} - x^{4}

f (x, y) = 3 - x + 2 y

What is the extreme f(x)=x+4/x+8,1<= x<= 8 ?
The extreme f(x)=x+4/x+8,1<= x<= 8 is Maximum(1,13),Minimum(2,12),Maximum(8, 33/2)