Hi! I've attached the graph in question. I need to graph the derivative of this function. I understand how to graph the derivative of a point, but I'm not sure what to do beyond that. How do I show the nondifferentiable points? Do I connect the points I do have? I'm not sure what to do next. Thanks!
Derivative Graph of non-continous function (am working from a picture, not a function statement)
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pka
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Do not add to the given graph.
You should know that a function has no derivative at points of discontinuity.
You should also know that a function has no derivative at "sharp" points.
The derivative along an open line segment is constant( the slope).
Along the "curve" you have to estimate the slope of tangent lines.
pka
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Yes I in fact said that. You will have a graph on each of \(\displaystyle (-6,-4),\;(-4,-2),\;(-2,2),\;(2,4),\;\&\;(4,6)\).
On the first two and last two the graphs are constant.
Steven G
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I am not sure why you are troubled at points where you know that there are no derivatives for the original function.
Say that f(x) is the function you want to draw the derivative of and suppose f(x) is not differentiable at x=7.
Now what value can you put for f' (7). If you say it is 11, then you are saying that the derivative of f(x) at x= 7 is 11. But this is not true as f(x) is not differentiable at x=7. So what do you put at x=7. How about 3/4? That is wrong for the same reason that 11 is wrong. So you put nothing for f' (7).
Say that f(x) is the function you want to draw the derivative of and suppose f(x) is not differentiable at x=7.
Now what value can you put for f' (7). If you say it is 11, then you are saying that the derivative of f(x) at x= 7 is 11. But this is not true as f(x) is not differentiable at x=7. So what do you put at x=7. How about 3/4? That is wrong for the same reason that 11 is wrong. So you put nothing for f' (7).
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Dr.Peterson
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Are you saying that you have only plotted a few disconnected points for your answer, and no lines or curves at all? Then you issue may not be with the points with no derivative, but something else.
Please show us the graph you have plotted so far, so we can see better what you are asking about.
pka
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7 is not even in the domain of this question. So are you confused as to what question to which you are responding ?
Steven G
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I just looked at the graph and see that 7 is not in the domain. This is true and I can't argue otherwise. However I was talking in general, not about this specific function at all.
I still maintain that IF a function is not differentiable at x=7, then f' (7) does not exist.
If I understood the original post, the OP did not understand how to graph the derivative function where the original function did not have a derivative.
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HallsofIvy
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There will be no derivative at x= -4, -2, 2, and 4. You can show that by small open circles at the ends of the graphs reaching those x values.
Between x= -6 to -4, the graph is a straight line with slope -1. So what is the derivative between x= -6 and -4? Between x= -4 and -2, the graph is a straight line with slope -3. So what is the derivative between x= -4 and -2? Between x= s-2 and -1, the graph is almost a straight line with slope 3 but curves down a little near x= -1. The graph of derivative is a horizontal line at height 3 but drops a little below that near x= -1. Between x= -1 and x= 0, the graph curves down to the horizontal at x= 0. So the graph of the derivative is little less than 3 at x= -1, dropping smoothly down to 0 at x= 0. Between x= 0 and 1, the graph curves up from horizontal at x= 0 to what looks like a slope of perhaps a little less than 3 at x= 1. So the graph of the derivative curves up from 0, at x= 0, to almost 3, at x= 1. Between x= 1 and 2, the graph is almost a straight line with slope 3. So the graph of the derivative starts a little below 3 at x= 1 and rises to a little above 3 at x= 2. Between x= 2 and 4 the graph is a straight line with slope 3. The derivative between x= 2 and 4 is that constant. Finally, for x between 4 and 6 the graph is a straight line with slope -1. The derivative is that constant.
Between x= -6 to -4, the graph is a straight line with slope -1. So what is the derivative between x= -6 and -4? Between x= -4 and -2, the graph is a straight line with slope -3. So what is the derivative between x= -4 and -2? Between x= s-2 and -1, the graph is almost a straight line with slope 3 but curves down a little near x= -1. The graph of derivative is a horizontal line at height 3 but drops a little below that near x= -1. Between x= -1 and x= 0, the graph curves down to the horizontal at x= 0. So the graph of the derivative is little less than 3 at x= -1, dropping smoothly down to 0 at x= 0. Between x= 0 and 1, the graph curves up from horizontal at x= 0 to what looks like a slope of perhaps a little less than 3 at x= 1. So the graph of the derivative curves up from 0, at x= 0, to almost 3, at x= 1. Between x= 1 and 2, the graph is almost a straight line with slope 3. So the graph of the derivative starts a little below 3 at x= 1 and rises to a little above 3 at x= 2. Between x= 2 and 4 the graph is a straight line with slope 3. The derivative between x= 2 and 4 is that constant. Finally, for x between 4 and 6 the graph is a straight line with slope -1. The derivative is that constant.