Generating...                               s20quiz16_n19

Let

$\displaystyle f(x) = -x^2\,e^ {- x }-4\,x\,e^ {- x }-4\,e^ {- x }+4 $

Then answer the following questions.

  1. Find the critical numbers of $f(x)$.

    $x = -3 $, $1$ $x = -1 $, $3$ $x = -2 $, $0$ $x = 0 $, $2$

  2. Choose the correct table for I/D test.

    Interval $x < -1$ $-1 < x < 3$ $3 < x $
    $f'(x)$ pos neg pos

    Interval $x < -1$ $-1 < x < 3$ $3 < x $
    $f'(x)$ neg pos neg

    Interval $x < -2$ $-2 < x < 0$ $0 < x $
    $f'(x)$ pos neg pos

    Interval $x < -2$ $-2 < x < 0$ $0 < x $
    $f'(x)$ neg pos neg

  3. Choose the correct statement.

    $y = 4-25\,e^ {- 3 }$ is local minimum at $x = 3$ . $y = 4$ is local maximum at $x = -2 $ . $y = 4-e$ is local maximum at $x = -1 $ . $y = 0$ is local maximum at $x = 0 $ .

  4. Find $\displaystyle\lim_{x\to -\infty}f(x)$ and $\displaystyle\lim_{x\to \infty}f(x)$ for horizontal asymptotes.

    $\displaystyle\lim_{x\to -\infty}f(x) =$ 4 and $\displaystyle\lim_{x\to \infty}f(x) =$ $\displaystyle \infty $

    $\displaystyle\lim_{x\to -\infty}f(x) =$ $\displaystyle \infty $ and $\displaystyle\lim_{x\to \infty}f(x) =$ 4

    $\displaystyle\lim_{x\to -\infty}f(x) =$ 4 and $\displaystyle\lim_{x\to \infty}f(x) =$ $\displaystyle -\infty $

    $\displaystyle\lim_{x\to -\infty}f(x) =$ $\displaystyle -\infty $ and $\displaystyle\lim_{x\to \infty}f(x) =$ 4

  5. Sketch the graph of $y = f(x)$.

    Image s20quiz16_pick_plot0

    Image s20quiz16_pick_plot1

    Image s20quiz16_pick_plot2

    Image s20quiz16_pick_plot3


Department of Mathematics
Last modified: 2026-07-16