Question

The function $f$ given by $f(x)=x^3{e}^x$ is increasing on the interval

• A. $(0,\infty )$
• B. $(3,\infty )$
• C. $(-3,\infty )$
• D. $(-3,3)$
• E. $(-\infty ,-3)$

Answer 1

Answer: (C)

$f(x)=x^3{e}^x$
$f^{\prime }(x)=e^x\left[x^3+3x^2\right]$
$f^{\prime }(x)=0\Rightarrow x^2(x+3)=0$
$\Rightarrow x=0,x=-3$
$(-3,\infty )$