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Question

If the greatest value of the function f(x)=14x423x332x2+2;xϵ[2,4] is M, then find the value of [M]
(where [ ] denotes greatest integer function.)

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Solution

f(x)=x442x333x22+2
f(x)=x32x23x
=x(x3)(x+1)
Maxima at x=2
f(0)=2
f(2)=4+1636+2=163
f(4)=64128324+2=23
M=[163]=5

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