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Help (Attached below) Determine the extrema of below on the given interval

Mathematics
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i know we have to find the derivative and set it to zero
i got x= 8 and x= 2/9

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Other answers:

now to have the intervals, im a little lost on...
would there only be 2 intervals?
or 3? 0-2/9 then 2/9-8 and 8-infinity?
ok... so whats the derivative...?
9x^2-74x+16
then i set it to = 0
ok... so what are the solutions...?
x=8 and x=2/9
critical numbers
yep... so on [0, 4] substitute x = 0, 2/9 and 4 into the original equation and find the corresponding values...
why 4?
thanks
isn't 4 a y?
and what 8?
because the 2 critical numbers are 8 and 2/9
well (a) is asking for the location of that min and max on the interval x = 0 to x = 4 and as x = 2/9 is a critical point...you don't know its nature
ooooooh, 8 would be the other one
let me try it
so the value x =0 is f(0) = 2 x = 2/9 f(2/9) = 3.76 x = 4 f(4) = ?
-334
so the max is 3.76 and min is -334?
thats correct...
so just test x = -9, x = 8 and x = 9... and see what happens... I think x = 2/9 remains the max
its an add interval since x = -9 gives a very large negative number

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