Question

Function $f\left(x\right)=\frac{x^2-2}{\sqrt{1+x^2}}$

• A. is always increasing
• B. is always decreasing
• C. has exactly one point of minima
• D. has exactly one point of maxima

Answer 1

Answer: (C)

has exactly one point of minima

Above is the graph of given function and it shows that the function has exactly one minima

For $f\left(x\right)=\frac{x^2-2}{\sqrt{1+x^2}}$

$f^{\prime }\left(x\right)=\frac{x(x^2+4)}{(1+x^2{)}^{1.5}}$

$f^{\prime }\left(x\right)=0$ at $x=0$

$f^{\prime }(-1)=\frac{-5}{2\sqrt{2}}\therefore$ function is decreasing

$f^{\prime }\left(1\right)=\frac{5}{2\sqrt{2}}\therefore$ function is increasing

$\therefore f\left(x\right)$ has exactly one point of minima at $x=0$

Correct option is C