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$The\ maximum\ value\ of\\f(x)\ =\ 2x^3-9x^2+12x-3\ in\ the\ interval\ 0<=x<=3\ is\   $

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asked in Calculus by Loyal (9.2k points) | 316 views
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is it 6?
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the max value will be 6..
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Got the value 6 but if we do by differentiation method Maxima will occur at x=1 and the value obtained will for x=1 will be 2. So how do we know that maximum can occur at any other value also?
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When we say f(x) is maximum at x=a, we mean that it is greatest in neighborhood of a i.e [a-h,a+h]
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points are -2 and -1

So, inside 0 to 3 no maximum value possible

right?
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stationary points 2 and 1 only...
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2 is not possible at all
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1 possible

but with solution we are not getting it
+2

let me know if anything is wrong!!!

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yes , I done a mistake
So, they are asking for maximum value
which is not possible for 2
It is only possible for 1
right?
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yes for x= 2 function will have minimum value..
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yes, so 1 is correct ans
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for x =1, we didn't have a maximum value, actually, they have given open interval range and for finding maximum we have to check those values too.That;s why i m checking at x=3 also which gives us maximum value as 6
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Ans is 6. Here we need to check all the values including 0 to 3 that at which value max occurs. Critical or stationary points(1,2) doesn't give the maximum but at 3 we get the maximum value of 6.
f(0) = -3
f(1) = 2
f(2) = 1
f(3) = 6
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In the given interval at the x=3 function will maximum value (6).
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answer is 6 ,which is at x=3

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