Let

$\displaystyle f(x) = \begin{cases} \displaystyle \left\vert x+1\right\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 $ .

    1 a + 1 −a − 1 −1 $\displaystyle \left\vert a+1\right\vert $

  2. Find the equation of the tangent line to $y = f(x)$ at $x = -{{1}\over{2}} $ .

    y = −x y = x + 1 y = 1 − x y = x

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

    $\displaystyle$    No $\displaystyle$    Yes

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

    $\displaystyle$   Does not exist 0 1 −1

  5. Find the derivative of $f(x)$ at $x = -{{1}\over{2}} $ .

    $\displaystyle {{1}\over{2}}$ $\displaystyle -{{1}\over{2}}$ 1 −1


Department of Mathematics
Last modified: 2025-03-29