Q. The minimum value of $x^{2} + \frac{1}{1 + x^{2}}\ is\ at$
A) $x = 0$
B) $x = 1\$
C) $x = 4$
D) $x = 3$
Explanation
(a)
Let $f(x) = x^{2} + \frac{1}{1 + x^{2}}$
$f^{'}(x) = 2x - \frac{1}{\left( 1 + x^{2} \right)^{2}}.2x$
For a minimum, put $f^{'}(x) = 0\ \Rightarrow \ \ \ x = 0$
So, the function has minimum value at $x = 0.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.