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Abs min/max

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Willy Wisp

Scholar

Karma Points: 276

Date Posted: 7/24/2008 8:07:26 PM Status: Live

Asker's Rating: Lifesaver

Response:

to find the min and max on a closed interval, you need to find the critical points first

the critical points are where f ' (x) = 0

f '(x) = -2x + 3 = 0
-2x = -3
x = 3/2

then test that value and the end points in f (x)

f (1) = -1 + 3 = 2
f (3/2) = -9/4 + 9/2 = 9/4
f (3) = -9 + 9 = 0

this shows that the max occurs at x = 3/2
and the min occurs at x = 3

Be Kind, Rewind.

Altair

Oracle

Karma Points: 13,127

Date Posted: 7/24/2008 8:43:37 PM Status: Live

Asker's Rating: Helpful

Response:

let us consider f'(x) = 0 to find the extrame values

f'(x) = -2x + 3 = 0

=> x = 3/2

let us also consider:

f"(x) = -2 < 0, so x = 3/2 is local maximum value

now we consider the endpoints

f(1)=-1+3=2

f(3) = -9+9=0

f(3/2)=-(3/2)² + 3(3/2) =9/2

The absolute max occurs at x = 3/2

and The absolute min occurs at x = 3

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Abs min/max

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