CPM Homework Help : CALC Problem 8-128

Multiple Choice: Given $f(x) =|4 - x ^ { 2 }|$ , $f^\prime(x)$ is:

$| \frac { - 2 x } { 4 - x ^ { 2 } }|$

$| \frac { 2 x } { 4 - x ^ { 2 } }|$

$\frac { 2 x } { | x ^ { 2 } - 4 | }$

$\frac { 2 x } { x ^ { 2 } - 4 }$

$\frac { 1 } { | x - 2 | }$

Hint:

Rewrite $f(x)$ as a piecewise function with boundary points at $x = −2$ and $x = 2$ . There will be three pieces. Though each piece needs to be differentiated separately, you will find that all three pieces have the same derivative!