Generating...                               quiz07_n18

Let

$\displaystyle f(x) = \begin{cases} \displaystyle {{1}\over{\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 = {{5}\over{2}} $ .

    −2 2 4 −4

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

    $\displaystyle \infty $ $\displaystyle$   Does not exist 0 $\displaystyle -\infty $

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

    $\displaystyle$    Yes $\displaystyle$    No

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

    $\displaystyle -{{1}\over{a-2}}$ $\displaystyle -{{1}\over{\left(a-2\right)^2}}$ $\displaystyle {{1}\over{\left\vert a-2\right\vert }}$ $\displaystyle {{1}\over{a-2}}$ $\displaystyle {{1}\over{\left(a-2\right)^2}}$

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

    y = 12 − 4x y = −4x y = 4x y = 4x + 12


Department of Mathematics
Last modified: 2025-06-19