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Question
f(x) = - (x-1)2+2 on R ?
Solution
Given: f(x) = − (x − 1)2 + 2
Now,
(x − 1)2 \[\geq\] 0 for all x \[\in\] R
\[\Rightarrow\] f(x) = − (x − 1)2 + 2 \[\leq\] 2 for all x \[\in\] R
The maximum value of f(x) is attained when (x − 1) = 0.
(x − 1) = 0
⇒ x = 1
Therefore, the maximum value of f (x) = 2
Since f(x) can be reduced, the minimum value does not exist, which is evident in the graph also.
Hence, function f does not have a minimum value.
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