What is the extreme f(x)=x+9/x+4,1<= x<= 18 ?

The extreme f(x)=x+9/x+4,1<= x<= 18 is Maximum(1,14),Minimum(3,10),Maximum(18, 45/2)

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extreme f(x)=x+9/x+4,1<= x<= 18

extreme points

f (x) = x + \frac{9}{x} + 4, 1 \leq x \leq 18

Maximum (1, 14), Minimum (3, 10), Maximum (18, \frac{45}{2})

Solution steps

Find the critical points:

x = 1, x = 3, x = 18

Domain of

x + \frac{9}{x} + 4, 1 \leq x \leq 18 : 1 \leq x \leq 18

Find intervals:

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < 18

Plug the extreme point

x = 1

into

x + \frac{9}{x} + 4 \Rightarrow y = 14

Maximum (1, 14)

Plug the extreme point

x = 3

into

x + \frac{9}{x} + 4 \Rightarrow y = 10

Minimum (3, 10)

Plug the extreme point

x = 18

into

x + \frac{9}{x} + 4 \Rightarrow y = \frac{45}{2}

Maximum (18, \frac{45}{2})

Maximum (1, 14), Minimum (3, 10), Maximum (18, \frac{45}{2})

f (x) = - 2 x + 3 ln (2 x)

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

f (x) = 16 x + 9 x^{- 1}

- 1683 x^{2} + 83000 x + 10000

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

What is the extreme f(x)=x+9/x+4,1<= x<= 18 ?
The extreme f(x)=x+9/x+4,1<= x<= 18 is Maximum(1,14),Minimum(3,10),Maximum(18, 45/2)