I'm a little confused

f(x) = |x|^2 - 4|x|

I know that gives the equations of:
x^2 - 4x and
x^2 + 4x

and you can differentiate them, but which equation corresponds to which part of the graph?

Thanks in advance

Originally Posted by freswood

I'm a little confused

f(x) = |x|^2 - 4|x|

I know that gives the equations of:
x^2 - 4x and
x^2 + 4x

and you can differentiate them, but which equation corresponds to which part of the graph?

Thanks in advance

When $\displaystyle x\ge 0$:

$\displaystyle |x|^2 - 4|x|=x^2-4x$.

When $\displaystyle x\le 0$:

$\displaystyle |x|^2 - 4|x|=x^2+4x$.

As a reality check you can always try plugging in numbers and seeing what
you get.

RonL

Hello, freswood!

Find the derivtive of: $\displaystyle f(x) \:= \:|x|^2 - 4|x|$

This is equivalent to the piecewise function: $\displaystyle f(x)\:=\:\left\{\begin{array}{cc} x^2 - 4x & x \geq 0 \\ x^2 + 4x & x < 0\end{array}$

Differentiate them for both cases.

You can check your results against the graph.

Code:

                      |
        *             |             *
                      |
         *            |            *
      - - * - - - - - * - - - - - * - -
         -4 *       * | *       * 4
               * *    |    * *
                      |

Originally Posted by Soroban

Differentiate them for both cases.

differention of |x|=|x|/x
where x is not equal to 0

Thanks!

What confused me is that for something like |x^2 - 4x| one applies to y>0 and the other to y < 0.

as in x < 0 U x > 4
and 0<x<4

Can anyone explain the difference between the two?