What is the extreme f(x)=x+((1))/((x)),0.2<= x<= 4 ?

The extreme f(x)=x+((1))/((x)),0.2<= x<= 4 is Maximum(0.2,5.2),Minimum(1,2),Maximum(4, 17/4)

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extreme f(x)=x+((1))/((x)),0.2<= x<= 4

extreme points

f (x) = x + \frac{( 1 )}{( x )}, 0.2 \leq x \leq 4

Maximum (0.2, 5.2), Minimum (1, 2), Maximum (4, \frac{17}{4})

Solution steps

Find the critical points:

x = 0.2, x = 1, x = 4

Domain of

x + \frac{1}{x}, 0.2 \leq x \leq 4 : 0.2 \leq x \leq 4

Find intervals:

Decreasing

: 0.2 < x < 1,

Increasing

: 1 < x < 4

Plug the extreme point

x = 0.2

into

x + \frac{1}{x} \Rightarrow y = 5.2

Maximum (0.2, 5.2)

Plug the extreme point

x = 1

into

x + \frac{1}{x} \Rightarrow y = 2

Minimum (1, 2)

Plug the extreme point

x = 4

into

x + \frac{1}{x} \Rightarrow y = \frac{17}{4}

Maximum (4, \frac{17}{4})

Maximum (0.2, 5.2), Minimum (1, 2), Maximum (4, \frac{17}{4})

f (x, y) = ln (1 + 4 x^{2} + 6 y^{2})

f (x) = x^{2} - 6 x y + 2 y^{2} + 10 x + 2 y - 5

25 x

f (x) = x - \frac{250}{x}

f (x) = - 25 x^{2} - 25 y^{2} + 200 x + 200 y + 200

What is the extreme f(x)=x+((1))/((x)),0.2<= x<= 4 ?
The extreme f(x)=x+((1))/((x)),0.2<= x<= 4 is Maximum(0.2,5.2),Minimum(1,2),Maximum(4, 17/4)