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Question

Find the maximum and minimum values, if any, of the following function given by, 

f(x)=(x1)2+10


Solution

Given, function is f(x)=(x1)2+10
It can be observed that (x1)20 for all xϵR
(x1)20 for every xϵR
Therefore, f(x)=(x1)2+1010 for every xϵR
The maximum value of f is attained when (x-1)=0
i.e., (x1)=0x=1Maximum value of f=f(1)=(11)2+10=10
For any value of x, f(x)10, hence function f does not have a particular minimum value.

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