#### 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.

Is there an error in this question or solution?

Solution F(X)=(X-1)2+2 on R ? Concept: Graph of Maxima and Minima.