What is the extreme (x^3+38x+128)/x ,1<= x<= 10 ?

The extreme (x^3+38x+128)/x ,1<= x<= 10 is Maximum(1,167),Minimum(4,86),Maximum(10, 754/5)

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extreme (x^3+38x+128)/x ,1<= x<= 10

extreme

Maximum (1, 167), Minimum (4, 86), Maximum (10, \frac{754}{5})

Solution steps

Find the critical points:

x = 1, x = 4, x = 10

Domain of

\frac{x ^{3} + 38 x + 128}{x}, 1 \leq x \leq 10 : 1 \leq x \leq 10

Find intervals:

Decreasing

: 1 < x < 4,

Increasing

: 4 < x < 10

Plug the extreme point

x = 1

into

\frac{x ^{3} + 38 x + 128}{x} \Rightarrow y = 167

Maximum (1, 167)

Plug the extreme point

x = 4

into

\frac{x ^{3} + 38 x + 128}{x} \Rightarrow y = 86

Minimum (4, 86)

Plug the extreme point

x = 10

into

\frac{x ^{3} + 38 x + 128}{x} \Rightarrow y = \frac{754}{5}

Maximum (10, \frac{754}{5})

Maximum (1, 167), Minimum (4, 86), Maximum (10, \frac{754}{5})

What is the extreme (x^3+38x+128)/x ,1<= x<= 10 ?
The extreme (x^3+38x+128)/x ,1<= x<= 10 is Maximum(1,167),Minimum(4,86),Maximum(10, 754/5)