Question 997829
So far I have:
f'(x) = 4x - 9
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At the min or max, f'(x) = 0
4x-9 = 0
x = 9/4
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f(9/4) = 2*81/16 - 9*9/4
= 81/8
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It's a parabola in x.  The x^2 term is positive --> opens upward
--> a minimum.
The 1st derivative is linear --> 1 extreme.
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f(x) = x = 4/9
If I plug back into the original function I can find either the max or min value.

f(4/9) = 2(4/9)^2 - 9(4/9) = - 10.125 (calculator) 
However, how do I know whether this is the max or min value without a graphical refrence?

Also, isn't there a rule with extrema stating that since the interval notation is [0,9] that I can use the 9? if so why not the 0. This rule keeps tripping me up.
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9/8 is between 0 and 9, so that's not an issue.