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
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 . . .