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. Find $f'(a)$ when $a$    > $-1 $ .

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

  2. Find the equation of the tangent line to $y = f(x)$ at $x = 2 $ .

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

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

    6 9 −9 −6

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

    $\displaystyle$   Does not exist 1 −1 0

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

    $\displaystyle$    No $\displaystyle$    Yes


Department of Mathematics
Last modified: 2026-08-20