Question

Find the intervals of monotonicity and the points of extremum of the following functions (426-427).
$y=x{e}^{-3x}$

Answer 1

$y={xe}^{-3x}$

$y^1=\frac{dy}{dx}={xe}^{-3x}(-3)+e^{-3x}$

$=e^{-3x}(-3x+1)$

For extension, $y^1=0$

$\Rightarrow x=\infty ,\left(1/3\right)$

As $e^{-3x}$ is decreasing function, so its monotonic function in interval $(\frac{1}{3},\infty )$