Question

The point of inflection for $y=f\left(x\right)=x{e}^x$ is:

• A. $0$
• B. $-2$
• C. $2$
• D. $-1$

Answer 1

The correct option is B $-2$

Given: $f\left(x\right)=x{e}^x$
$\Rightarrow f^{\prime }\left(x\right)=e^x(x+1)$
$\Rightarrow f^{\prime \prime }\left(x\right)=e^x(x+1+1)=e^x(x+2)$
Clearly, the second derivative is zero at $x=-2$ and also it changes sign at $x=-2$. Hence it is a point of inflection.