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Question

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x)=2x3−9x2+12x+5 in the interval [0,3]. Then M−m is equal to.

A
1
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B
5
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C
4
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D
9
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Solution

The correct option is D 9
f(x)=2x39x2+12x+5
f(x)=6x218x+12=0
x23x+2=0
x=1 or x=2


Thus, f(1)=29+12+5=10
And f(2)=2(2)39(2)2+12(2)+5=1636+24+5
Thus f(2)=9

Now, also we need to check the values of the function at x=0 and x=3

f(0)=5

Also, f(3)=2(3)39(3)2+12(3)+5
Thus f(3)=9581=14

f′′(x)=12x18

Thus M=14 and m=5 since M and m are the absolute Maxima and minima of the given function.

Thus Mm=145=9


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