`f(x) = 12 + 4x - x^2, [0, 5]` Find the absolute maximum and minimum values of f on the given interval

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Given: `f(x)=12+4x-x^2,[0,5]`

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)=4-2x=0`

`4=2x`

`2=x`

The value x=2 is a critical number. Plug in the x=2 and the endpoints of the interval into the original f(x) function.

f(0)=12

f(2)=16

f(5)=7

...

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Given: `f(x)=12+4x-x^2,[0,5]`

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)=4-2x=0`

`4=2x`

`2=x`

The value x=2 is a critical number. Plug in the x=2 and the endpoints of the interval into the original f(x) function.

f(0)=12

f(2)=16

f(5)=7

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

The absolute maximum occurs at the point (2, 16).

The absolute minimum occurs at the point (5, 7).

Approved by eNotes Editorial Team