What is the extreme f(x)=x+4/x ,1<= x<= 10 ?

The extreme f(x)=x+4/x ,1<= x<= 10 is Maximum(1,5),Minimum(2,4),Maximum(10, 52/5)

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extreme f(x)=x+4/x ,1<= x<= 10

extreme points

f (x) = x + \frac{4}{x}, 1 \leq x \leq 10

Maximum (1, 5), Minimum (2, 4), Maximum (10, \frac{52}{5})

Solution steps

Find the critical points:

x = 1, x = 2, x = 10

Domain of

x + \frac{4}{x}, 1 \leq x \leq 10 : 1 \leq x \leq 10

Find intervals:

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < 10

Plug the extreme point

x = 1

into

x + \frac{4}{x} \Rightarrow y = 5

Maximum (1, 5)

Plug the extreme point

x = 2

into

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

Minimum (2, 4)

Plug the extreme point

x = 10

into

x + \frac{4}{x} \Rightarrow y = \frac{52}{5}

Maximum (10, \frac{52}{5})

Maximum (1, 5), Minimum (2, 4), Maximum (10, \frac{52}{5})

2 θ - 3 sin (θ)

f (x) = x^{2} + 2 x - 30

- \frac{1}{x ^{2} + 49} - \frac{1}{( x - 5 ) ^{2} + 4}

f (x) = x \cdot (ln (x))^{2}

f (x) = x [36 - 2 (x)]^{2}

What is the extreme f(x)=x+4/x ,1<= x<= 10 ?
The extreme f(x)=x+4/x ,1<= x<= 10 is Maximum(1,5),Minimum(2,4),Maximum(10, 52/5)