Generating...                               quiz07_n10

Let

$\displaystyle f(x) = \begin{cases} \displaystyle \left\vert x-1\right\vert \,\... ...-1\right) & \mbox{ if $x \neq 1 $ } \\ 0 & \mbox{ if $x = 1 $ } \end{cases}$

Then answer the following questions.

  1. Find the derivative of $f(x)$ at $x = 4 $ .

    −6 6 −9 9

  2. Is $f(x)$ differentiable at $x = 1$ ?

    $\displaystyle$    Yes $\displaystyle$    No

  3. Find $f'(a)$ when $a$    > $1 $ .

    $\displaystyle -\left(a-1\right)^2$ $\displaystyle \left\vert a-1\right\vert \,\left(a-1\right)$ 2(a − 1) $\displaystyle \left(a-1\right)^2$ −2(a − 1)

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

    −1 0 $\displaystyle$   Does not exist 1

  5. Find the equation of the tangent line to $y = f(x)$ at $x = 4 $ .

    y = 6x − 15 y = −6x − 15 y = −6x y = 6x


Department of Mathematics
Last modified: 2026-03-24