1. ## Derivative graph

Hi, I have this graph of a function but it doesn't give the equation for the function. The question wants me to graph the derivative but I don't know how. I am able to count where the points are so can anyone help me?

2. Originally Posted by Blueazulim06
Hi, I have this graph of a function but it doesn't give the equation for the function. The question wants me to graph the derivative but I don't know how. I am able to count where the points are so can anyone help me?
Recall that the derivative of a function at a point is the slope of the tangent line to the curve at that point. So sketch the tangent line at a point on the graph and measure the slope of that line. That will give you the value of the derivative at that point.

A handy trick to remember while you are doing this is that any point where the function has a relative maximum or minimum is going to be a point where the derivative graph crosses (or perhaps touches) the x-axis. (Because the derivative is zero there.) The same comment holds for inflection points as well if you are practiced enough to be able to spot those.

-Dan

3. Hello, Blueazulim06!

Topsquark gave you the best advice.
Let me try to make it clearer . . .

I have this graph of a function, but not the equation for the function.
The question wants me to graph the derivative.

Suppose your graph looks like this:
Code:
                *
*           *

*                 *

*                   *                 *

*               *

*         *
*

Estimate the slope at a number of points.
Code:
               m=0
m=1      -*-    m=-1
*           *
/               \
m=2 *                 * m=-2
/                   \
*                   *                   *

*                 * m=2
\             /
m=-1 *           * m=1
\   -*-   /
m=0

Those are the values we plot on the "derivative graph".
Code:
      |
2+   *                       *
|
|
1+      *                 *
|
|
- + - - - - * - - - - - * - -
|
|
-1             *     *
|
|
-2+               *
|

Hope this helps . . .

4. Originally Posted by Soroban
Hello, Blueazulim06!

Topsquark gave you the best advice.
Let me try to make it clearer . . .

Suppose your graph looks like this:
Code:
                *
*           *

*                 *

*                   *                 *

*               *

*         *
*
Estimate the slope at a number of points.
Code:
               m=0
m=1      -*-    m=-1
*           *
/               \
m=2 *                 * m=-2
/                   \
*                   *                   *

*                 * m=2
\             /
m=-1 *           * m=1
\   -*-   /
m=0
Those are the values we plot on the "derivative graph".
Code:
      |
2+   *                       *
|
|
1+      *                 *
|
|
- + - - - - * - - - - - * - -
|
|
-1             *     *
|
|
-2+               *
|
Hope this helps . . .
Thanks Soroban. I still haven't gotten any graphing software.

-Dan