First slide

Maxima and minima

Question

$If f (x) = \frac{x^{2} - 1}{x^{2} + 1}, for every real number, then minimum value of f$

Moderate

A

does not exist
B

is not attained even though f is bounded
C

is equal to 1
D

is equal to -1

Solution

$We have f (x) = 1 - \frac{2}{x^{2} + 1}$
$f (x) will be minimum if 2 / (x^{2} + 1) is maximum i.e. if$ $x^{2} + 1 is least i.e. when x = 0 . Thus minimum value of$ $f (x) i s f (0) = - 1$

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