Generating...                               quiz07_n13

Let

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

Then answer the following questions.

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

    −1 $\displaystyle$   Does not exist 0 1

  2. Find $f'(a)$ when $a$    > $2 $ .

    2(a − 2) −2(a − 2) $\displaystyle \left\vert a-2\right\vert \,\left(a-2\right)$ $\displaystyle \left(a-2\right)^2$ $\displaystyle -\left(a-2\right)^2$

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

    $\displaystyle$    No $\displaystyle$    Yes

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

    3 −3 $\displaystyle -{{9}\over{4}}$ $\displaystyle {{9}\over{4}}$

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

    $\displaystyle y=3\,x-{{33}\over{4}}$ y = 3x $\displaystyle y=-3\,x-{{33}\over{4}}$ y = −3x


Department of Mathematics
Last modified: 2026-09-10