MCQ
The point for the curve $y = x{e^x}$
- ✓$x = - 1$ is minimum
- B$x = 0$ is minimum
- C$x = - 1$ is maximum
- D$x = 0$ is maximum
✓
Answer
Correct option: A.
$x = - 1$ is minimum
a
(a) Given equation (curve) $y = x{e^x}$
(a) Given equation (curve) $y = x{e^x}$
$\therefore \frac{{dy}}{{dx}} = x{e^x} + {e^x} = {e^x}(1 + x)$ and $\frac{{{d^2}y}}{{d{x^2}}} = (x + 2)\,{e^x}$
For maximum or minimum value of $f(x)$,
==> $\frac{{dy}}{{dx}} = 0 \Rightarrow x = - 1$.
$\therefore {\left\{ {f''(x)} \right\}_{x = - 1}} = + ve$
Hence $f(x)$is minimum at $x = - 1$.
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