Question

The graph of $y=e^{x^2}$ is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

Given curve : $y=e^{x^2}$
Now, properties of graph :
$\left(i\right)$ Domain $\in R$ and Range $\in [1,\infty ).$
$\left(ii\right)y(-x)=y\left(x\right)\Rightarrow$ symmetric about $Y-$axis.
and $y\left(0\right)=1$
$\left(iii\right)y^{\prime }=2x{e}^{x^2}$
$\Rightarrow y^{\prime }=0,$ gives $x=0$ (Local minimum)
$\Rightarrow$ for $x<0,y^{\prime }<0$ (decreasing)
for $x>0,y^{\prime }>0$ (increasing)
$\left(iv\right)y^{\prime \prime }=e^{x^2}(4x^2+2)>0$ (concave up)
Now plotting the graph :