Question

The graph of $y=\frac{1}{x^2}$ is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Given : $y=\frac{1}{x^2},$ Domain $\in R-\left\{0\right\}$ and range $\in R^{+}$
Now, $f(-x)=f\left(x\right)\Rightarrow$ symmetric about $Y-$axis,
and $y^{\prime }=-\frac{2}{x^3}$
For $y^{\prime }>0,x<0$ (increasing)
For $y^{\prime }<0,x>0$ (decreasing)
$\Rightarrow y^{\prime \prime }=\frac{6}{x^4}$ (Concave up)
Also, $x\to 0^{+},y\to \infty \&x\to 0^{-},y\to \infty$
and $x\to +\infty ,y\to 0\&x\to -\infty ,y\to 0$
Now, plotting the graph :