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Question

Find the greatest and the least values of the following functions.
f(x)=2x33x212x+1 on the interval [-1, 5].

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Solution

f(x)=2x33x212x+1
f(x)=6x26x12=0(x2)(x+1)=0
x=2,1
f′′(x)=12x6
f′′(2)=18>0,Hence f(2)=19 is the minimum
f′′(1)=18>0,Hence f(1)=8 is the maximum


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