`f(x) = x + 1/x, [0.2, 4]` Find the absolute maximum and minimum values of f on the given interval

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Chapter 4, 4.1 - Problem 53 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Given: `f(x)=x+(1/x),[0.2,4]`

Find the critical value(s) of the function by setting the first derivative equal to zero and solving for the x value(s).

`f'(x)=1-(1/x^2)=0`

`1=(1/x^2)`

`x^2=1`

`x=1,x=-1`

Plug in the x=1 and the endpoints of the given interval into the original f(x) function. The x=-1 will not be used because it is not in the given interval

[0.2, 4].

f(1)=2

f(0.2)=5.2

f(4)=4.25

Examine the f(x) values to determine the absolute maximum and absolute minimum.

The absolute maximum occurs at the coordinate (0.2, 5.2).

The absolute minimum occurs at the coordinate (1, 2).

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