Question

f(x) = - (x-1)²+2 on R ?

Answer 1

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.