`f(x) = (3/4)x + 2, [0,4]` Find the absolute extrema of the function on the closed interval.

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Chapter 3, 3.1 - Problem 18 - 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)=(3/4)x+2,[0, 4]`

First find the critical value(s) of the function (if any exist). To find the critical value(s) of the function, set the derivative equal to zero and solve for the x-value(s).

`f'(x)=(3/4)=0`

A critical value will not exist for this function.

Plug in the critical value(s) (if any) and the endpoints of the closed interval into the f(x) function.

`f(x)=(3/4)x+2`

`f(0)=(3/4)(0)+2=2`

`f(4)=(3/4)(4)+2=5`

Examine the f(x) values.

The absolute maximum of the function is at the point (4, 5).

The absolute minimum of the function is at the point (0, 2).

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