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In GeoGebra, is there a way to define a function of two variables which is the pointwise minimum of two functions.

Like h(x, y):= min(x² + y², x + y).

(The GeoGebra Min command does something different.)

I could work around by means of the abs function, whichis available, using min(a, b) = (a + b - |a - b|) / 2, but this is not very convenient (actually I need to take the minimum of more than two functions).

  • Hmm, I wonder whether the Extremum Command could help somehow.. – gsamaras Aug 24 '17 at 08:21
  • @gsamaras No, I am not after the extrema. Pointwise minima between the two functions. –  Aug 24 '17 at 08:23
  • I was trying something like `Min( Min(x² + y², 0, 1), Min(x + y, 2, 3) )`, but that didn't work out...I read about custom tools, which might be helpful in this case.. – gsamaras Aug 24 '17 at 08:46

3 Answers3

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You could use a Conditional Function to create a piecewise function that is equal to f(x) if f(x) < g(x) and g(x) otherwise. The definition of this is:

If(f(x) < g(x), f, g)

Here's an example of this in action.

jtimmons
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  • Thanks, that's cleaner than my approach with the absolute value. But still inconvenient to take the minimum of several functions, because f and g need to appear twice in the expression, which makes it grow fat very quickly. –  Jan 16 '18 at 08:11
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One option: Plot a point A on the x-axis. Compute F=min({f(x(A)),g(x(A)),h(x(A))}). Plot B=(x(A),F). Create Locus(B,A).

Gerry Wojnar
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If you want the minimum of two functions f(x) and g(x) then you can define (f(x) + g(x) - abs(f(x) - g(x)))/2

nicholasfor
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