0
$\begingroup$

A very interesting problem from here.

I got the algebra in less than a minute with all 6 solutions (integers). But was puzzled a bit that the graph only gives 4. As now I have waken up and tried it on my own, these are the findings.

Plot[(x^2 - 7 x + 11)^(x^2 - 13 x + 42), {x, 0, 8}, Frame -> True,  PlotRange -> {{0, 8}, {-0.25, 3}},  GridLines -> {Range[8], {-1, 0, 1}}, Mesh -> All] 

enter image description here

Obviously there is a whole region "missing". Then I tried to plot it as a discrete function.

DiscretePlot[(x^2 - 7 x + 11)^(x^2 - 13 x + 42), {x, 0, 8},  Frame -> True, PlotRange -> {{0, 8}, {-0.25, 3}},  GridLines -> {Range[8], {-1, 0, 1}}] 

enter image description here

I have tried to tweak Mesh, PlotPoints, ect.

I know what's going on mathematically in that region, but is there a better way to explore this function when we plot it, so that we don't miss special points, especially "important" points like integer numbers that are still valid?

In comparison

NSolve[(x^2 - 7 x + 11)^(x^2 - 13 x + 42) == 1, x, Reals]

{{x -> 2.}, {x -> 5.}, {x -> 6.}, {x -> 7.}}

Failed to give all solutions in this case while

Solve[(x^2 - 7 x + 11)^(x^2 - 13 x + 42) == 1, x, Reals]

{{x -> 2}, {x -> 3}, {x -> 4}, {x -> 5}, {x -> 6}, {x -> 7}}

does give all correct answers.

$\endgroup$
  • 3
    $\begingroup$ Plot[ReIm[(x^2-7 x+11)^(x^2-13 x+42)], {x, 2, 5},PlotRange->All] $\endgroup$ – Bill Jan 4 at 19:00

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.