What is the extreme f(x)=x+(25)/x ,0.2<= x<= 20 ?

The extreme f(x)=x+(25)/x ,0.2<= x<= 20 is Maximum(0.2,125.2),Minimum(5,10),Maximum(20, 85/4)

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extreme f(x)=x+(25)/x ,0.2<= x<= 20

extreme points

f (x) = x + \frac{25}{x}, 0.2 \leq x \leq 20

Maximum (0.2, 125.2), Minimum (5, 10), Maximum (20, \frac{85}{4})

Solution steps

Find the critical points:

x = 0.2, x = 5, x = 20

Domain of

x + \frac{25}{x}, 0.2 \leq x \leq 20 : 0.2 \leq x \leq 20

Find intervals:

Decreasing

: 0.2 < x < 5,

Increasing

: 5 < x < 20

Plug the extreme point

x = 0.2

into

x + \frac{25}{x} \Rightarrow y = 125.2

Maximum (0.2, 125.2)

Plug the extreme point

x = 5

into

x + \frac{25}{x} \Rightarrow y = 10

Minimum (5, 10)

Plug the extreme point

x = 20

into

x + \frac{25}{x} \Rightarrow y = \frac{85}{4}

Maximum (20, \frac{85}{4})

Maximum (0.2, 125.2), Minimum (5, 10), Maximum (20, \frac{85}{4})

y = x^{3} - 30 x^{2} + 6000

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

f (x) - x^{4} - 8 x^{2} + 1

f (x) = x^{3} - 12 x + 17

f (x) = x^{3} + 2 x^{2} - 20 x

What is the extreme f(x)=x+(25)/x ,0.2<= x<= 20 ?
The extreme f(x)=x+(25)/x ,0.2<= x<= 20 is Maximum(0.2,125.2),Minimum(5,10),Maximum(20, 85/4)