# Picewise derivative problems

1. Dec 4, 2008

### farmd684

1. The problem statement, all variables and given/known data
y=|x^2-4|+2 find f,relative extrema,minima.

2. Relevant equations
Detailed graphing of
y={ 9-x,x<=3
x^2-3,x>3

using derivatives

3. The attempt at a solution
I m not sure how to do this sort of prblems.

2. Dec 5, 2008

### CompuChip

Usually, it works to get rid of the absolute value signs. So first solve where x^2 - 4 is positive and negative and treat those cases separately.

Simple example: derive y = |x|.
1) For x > 0 (or x = 0), this reads y = x. Then the derivative is y' = 1.
2) For x < 0, it means y = -x. Then the derivative is y' = -1.

Afterwards, you may try to find a general formula. For example, if you are used to working with such things, you might write something like: y' = sign(x) for x non-zero (and for x = 0, the derivative is undefined).

3. Dec 5, 2008

### HallsofIvy

Staff Emeritus
Graphing is the simplest thing to do. As CompuChip said, get rid of the absolute value signs. x2- 4 is 0 at x= -2 and x= 2. Between -2 and 2, x2- 4 is negative and so |x2- 4|= 4- x2. Graph y= x2- 4 up to x= -2, then y= 4- x2 for x between -2 and 2, and, finally, graph y= x2- 4 for x> 2.

That is the same, of course, as graphing y= x2- 4, then "flipping" the part of the graph below the y-axis up. It should be easy to see where relative max and min are.

4. Dec 5, 2008

### CompuChip

And for your real question, don't forget the +2

5. Dec 5, 2008

### farmd684

Thanks i have understood that.I know how to graph piecewise functions but i m confused how to draw them by using the method of derivative i mean by f and f increasing part decreasing part,concave up down and so on.