PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# F(X)=(X-1)2+2 on R ? - PUC Karnataka Science Class 12 - Mathematics

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