`f(x) = 3 - x, [-1,2]` Find the absolute extrema of the function on the closed interval.

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Chapter 3, 3.1 - Problem 17 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: f(x)=3-x,[-1,2]

First find the critical values of the function. To find the critical values of the function (if one exists), set the derivative of the function equal to zero and solve for the x value(s).

f'(x)=-1=0

There will not be a critical x value for the given function.

Plug in the critical x value(s) (if one exists), and the endpoints of the closed interval into the original f(x) function.

f(x)=3-x

f(-1)=3-(-1)=4

f(2)=3-2=1

Examine the f(x) values.

The absolute maximum of the function is the point (-1, 4)

The absolute minimum of the function is the point (2, 1)

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