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Question

Find the greatest and the least values of the following function.
f(x)=2x39x2+12x on the interval [0,3].

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Solution

f(x)=2x39x2+12x
f(x)=6x218x+12=0(x1)(x2)=0
x=1,2
f′′(x)=(2x3)6
f′′(1)=6<0 hence f(1)=5 is maximum
f′′(2)=6>0 hence f(2)=4 is minimum

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