Generating...                               quiz07_n5

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

    $\displaystyle$    No $\displaystyle$    Yes

  2. Find the derivative of $f(x)$ at $x = -1 $ .

    9 −6 6 −9

  3. Find the equation of the tangent line to $y = f(x)$ at $x = -1 $ .

    y = 6x y = 6x − 3 y = −6x y = −6x − 3

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

    0 1 $\displaystyle$   Does not exist −1

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

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


Department of Mathematics
Last modified: 2025-10-30