Question

For the curve $y=x{e}^x$, the point

• A. x = - 1 is a point of minimum
• B. x = 0 is a point of minimum
• C. x = - 1 is a point of maximum
• D. x = 0 is a point of maximum

Answer 1

Answer: (A)

Given, curve is $y=x{e}^x$
$\Rightarrow \frac{dy}{dx}=e^x+x{e}^x$
For maximum and minimum, put $\frac{dy}{dx}=0$
$\Rightarrow e^x(1+x)=0$
$\Rightarrow x=-1$
Now, $\frac{d^{2}y}{d{x}^2}=2e^x+x{e}^x$
At $x=-1,\frac{d^{2}y}{d{x}^2}=e^{-1}(2-1)>0$
Hence, $x=-1$ is a point of minimum.