Question

A curve $y=f(x)$ passing through the point $\left(1, \frac{1}{\sqrt{e}}\right)$ satisfies the differential equation $\frac{d y}{d x}+x^{-\frac{x^2}{2}}=0$. Then which of the following does not hold good?

• A. $f(x)$ is differentiable at $x=0$.
• B. $f(x)$ is symmetric w.r.t. the origin.
• C. $f(x)$ is increasing for $x<0$ and decreasing for $x >0$.
• D. $f ( x )$ has two inflection points.

Answer 1

Answer: (B)

$y=f(x)=e^{-\frac{x^2}{2}}$. The graph is as shown