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    <p>Could find the points via:</p> <pre><code>slope45s = h /. Map[First[Solve[D[#, h] == -1 &amp;&amp; h &gt;= 0, h]] &amp;, a[h]] </code></pre> <p>Out[12]= {0.623422, 0.415615, 0.311711, 0.249369, 0.207807, 0.178121, \ 0.155856}</p> <p>Here we put together the list of relevant points.</p> <pre><code>pts = Transpose[{slope45s, Tr[a[slope45s], List]}] </code></pre> <p>Can now plot in any number of ways. Here is one such.</p> <pre><code>p2 = ListPlot[pts, PlotRange -&gt; {{0, 4}, {0, -4}}, PlotStyle -&gt; {PointSize[.01], Red}]; p1 = Plot[a[h], {h, 0, 4}, PlotRange -&gt; {{0, 4}, {0, -4}}, AspectRatio -&gt; 1]; </code></pre> <p>Show[p1, p2]</p> <p>(Being new to this modern world-- or rather, of an age associated with an earlier civilization-- I do not know how to paste in an image.)</p> <p>(Okay, thanks Leonid. I think I have an image and also indented code.)</p> <p>(But why are we talking in parentheses??)</p> <p><img src="https://i.stack.imgur.com/bdTvX.gif" alt="enter image description here"> Daniel Lichtblau Wolfram Research</p> <p>Edit: I did not much like the picture I gave. Here is one I think is more descriptive.</p> <pre><code>makeSegment[pt_, slope_, len_] := Rotate[Line[{pt + {-len/2, 0}, pt + {len/2, 0}}], ArcTan[slope]] p2 = ListPlot[pts, PlotStyle -&gt; {PointSize[.01], Red}]; p1 = Plot[a[h], {h, 0, 4}, PlotRange -&gt; {{0, 2}, {0, -1}}, AspectRatio -&gt; 1]; p3 = Graphics[Map[{Orange, makeSegment[#, -1, .2]} &amp;, pts]]; Show[p1, p2, p3, AspectRatio -&gt; 1/2, ImageSize -&gt; 1000] </code></pre> <p><img src="https://i.stack.imgur.com/NJQ3J.gif" alt="enter image description here"></p>
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    1. POHow do you solve for the positive roots of a function and graph them as points on a plot of the function in mathematica?
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    1. USMr.Wizard
    1. USDaniel Lichtblau
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    1. CO@Daniel Lichtblau: there should be an icon in the set of icons at the top of the editor, for pasting an image. But it may depend on the reputation, I am not sure. I seem to remember that I could not initially post images either. Also, for the code - if you want it to be printed in the "code" font, all it takes is to tab it 4 spaces to the right (tab key itself does not work, so you have to use the space)
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      1. USLeonid Shifrin
    2. CO@Daniel It seems you merged two versions of the code (or some statements are missing)
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      1. USDr. belisarius
    3. CO@belisarius Sorry, you are correct (and worse, I deleted the notebook I had). The list of pts was constructed in a manner similar to Leonid's MapIndexed, but not so elegantly.
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