Generating...                               quiz07_n21

Let

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

Then answer the following questions.

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

    $\displaystyle$    No $\displaystyle$    Yes

  2. Find $f'(a)$ when $a$    < $-1 $ .

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

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

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

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

    9 6 −6 −9

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

    $\displaystyle$   Does not exist 1 0 −1


Department of Mathematics
Last modified: 2026-07-16