What is the extreme f(x)=x+(16)/x+6,1<= x<= 32 ?

The extreme f(x)=x+(16)/x+6,1<= x<= 32 is Maximum(1,23),Minimum(4,14),Maximum(32, 77/2)

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extreme f(x)=x+(16)/x+6,1<= x<= 32

extreme points

f (x) = x + \frac{16}{x} + 6, 1 \leq x \leq 32

Maximum (1, 23), Minimum (4, 14), Maximum (32, \frac{77}{2})

Solution steps

Find the critical points:

x = 1, x = 4, x = 32

Domain of

x + \frac{16}{x} + 6, 1 \leq x \leq 32 : 1 \leq x \leq 32

Find intervals:

Decreasing

: 1 < x < 4,

Increasing

: 4 < x < 32

Plug the extreme point

x = 1

into

x + \frac{16}{x} + 6 \Rightarrow y = 23

Maximum (1, 23)

Plug the extreme point

x = 4

into

x + \frac{16}{x} + 6 \Rightarrow y = 14

Minimum (4, 14)

Plug the extreme point

x = 32

into

x + \frac{16}{x} + 6 \Rightarrow y = \frac{77}{2}

Maximum (32, \frac{77}{2})

Maximum (1, 23), Minimum (4, 14), Maximum (32, \frac{77}{2})

f (x) = 3 x^{2} - 4 x + 1, 0 \leq x \leq 2

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

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

f (x y) = 2 x y - x^{2} - 2 y^{2} + 3 x + 4

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 17

What is the extreme f(x)=x+(16)/x+6,1<= x<= 32 ?
The extreme f(x)=x+(16)/x+6,1<= x<= 32 is Maximum(1,23),Minimum(4,14),Maximum(32, 77/2)