Generating...                               quiz07_n20

Let

$\displaystyle f(x) = \begin{cases} \displaystyle \left\vert x+2\right\vert & \mbox{ if $x \neq -2 $ } \\ 0 & \mbox{ if $x = -2 $ } \end{cases}$

Then answer the following questions.

  1. Find the derivative of $f(x)$ at $x = -{{7}\over{2}} $ .

    1 $\displaystyle {{3}\over{2}}$ −1 $\displaystyle -{{3}\over{2}}$

  2. Find the equation of the tangent line to $y = f(x)$ at $x = -{{7}\over{2}} $ .

    y = x y = −x y = −x − 2 y = x − 2

  3. Is $f(x)$ differentiable at $x = -2$ ?

    $\displaystyle$    Yes $\displaystyle$    No

  4. Find $\displaystyle\lim_{h\to 0} \frac{ f\left(h-2\right)-f\left(-2\right)}{h}$ .

    $\displaystyle$   Does not exist −1 0 1

  5. Find $f'(a)$ when $a$    < $-2 $ .

    −1 1 $\displaystyle \left\vert a+2\right\vert $ −a − 2 a + 2


Department of Mathematics
Last modified: 2026-03-24