How to graph the slope ?

summerhill

2009-02-24 1:42 pm

How do you graph the derivative (or the slope) of a function simply by looking at the graph ( the overall shape)??

I understand how to graph the slope of, let say, a parabola or an absolute-value function, but how do you graph the slope of those more complicated graphs? For instance, a lying 'S' shape ones and infinity ones??

What if you're given the derivative graph, how do you find the shape of original function?

Please explain as detail as possible. And all of the above are talking about the 'shape' of the graph, no need to specify the exact values and points.
Thanks in advance.

更新1:

The second step sounds a bit confusing. So you look for sections with increasing and decreasing slopes of the original graph in step 2?

更新2:

Increasing sections of original graph give f'>0 so the f' graph is above x-axis? Then negative derivative gives the opposite? Is that how you find the corresponding sections of f' graph?

回答 (1)

用戶10012

2009-02-24 4:36 pm

✔ 最佳答案

Step 1: From the giving graph, search for the turning points. These are the points where dy/dx = 0. That means, these are the x- intercepts on the dy/dx against x graph.
Step 2 : From the giving graph, look for those sections with positive slopes. These are the section where dy/dx is positive. Similarly, sections of the graph with negative slopes gives dy/dx < 0.
Step 3: Joining the points found in step 1 and line segments found in step 2 will give a sketch of the dy/dx against x curve.
If given the dy/dx curve to find the original curve, just doing the reverse of the above.

2009-02-24 08:40:03 補充：
For step 2, notice that steeper is the slope of the graph, larger is the absolute value of dy/dx.

2009-02-24 08:47:45 補充：
A lying S curve will give a reversed V shape dy/dx curve.

2009-02-24 08:56:03 補充：
Same method can be used to sketch y" curve if the y' curve is given.

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