The graph of y-1x2 is

Given : y=1x^2, Domain ∈ℝ {0} and range ∈ℝ^+ Now, f( x)=f(x)⇒ symmetric about Y axis, nbsp; and y'= 2x^3 For y' gt;0,x lt;0 (increasing) For y' lt;0,x ...

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Standard XII

Mathematics

Monotonically Increasing Functions

The graph of ...

Question

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

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Solution

Given : $y = \frac{1}{x^{2}},$ Domain $\in R - {0}$ and range $\in R^{+}$
Now, $f (- x) = f (x) \Rightarrow$ symmetric about $Y -$ axis,
and $y^{'} = - \frac{2}{x^{3}}$
For $y^{'} > 0, x < 0$ (increasing)
For $y^{'} < 0, x > 0$ (decreasing)
$\Rightarrow y^{''} = \frac{6}{x^{4}}$ (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 :

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The graph of y=1x2 is

Given : y=1x2, Domain ∈R−{0} and range ∈R+ Now, f(−x)=f(x)⇒ symmetric about Y−axis, and y′=−2x3 For y′>0,x<0 (increasing) For y′<0,x>0 (decreasing) ⇒y′′=6x4 (Concave up) Also, x→0+,y→∞ & x→0−,y→∞ and x→+∞,y→0 & x→−∞,y→0 Now, plotting the graph :

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