Generating...                               s20quiz16_n24

Let

$\displaystyle f(x) = x^2\,e^{x}-3\,x\,e^{x}+e^{x}+4 $

Then answer the following questions.

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

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

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

    Interval $x < 0$ $0 < x < 3$ $3 < x $
    $f'(x)$ neg pos neg

    Interval $x < -1$ $-1 < x < 2$ $2 < x $
    $f'(x)$ neg pos neg

    Interval $x < -1$ $-1 < x < 2$ $2 < x $
    $f'(x)$ pos neg pos

    Interval $x < 0$ $0 < x < 3$ $3 < x $
    $f'(x)$ pos neg pos

  3. Choose the correct statement.

    $y = 5$ is local maximum at $x = 0 $ . $y = 5\,e^ {- 1 }+4$ is local maximum at $x = -1 $ . $y = e^3+4$ is local minimum at $x = 3$ . $y = 4-e^2$ is local maximum at $x = 2$ .

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

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

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

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

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

  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: 2025-06-19