Manipulate the range of values for the variable in a Plot

Questions
,
1

I have the following code:
a := 0; b := 5;
fxsquared[x_] := x^2;
Plot[fxsquared[x], {x, a, b}]

I would like to use Manipulate to vary the values of a and b and see the plot change.
Is there any way to do that?

2

Do not set variables of constant values with :=, just use =

For the sake of Manipulate you do not need them at all. The following will give you the basic idea, and from there keep reading the documentation

Manipulate[Plot[Sin[x], {x, a, b}], {a, 0, 2 Pi}, {b, 3 Pi, 10 Pi}]
3

Thank you! That worked. I’m a novice and learning as I go. I now have this code functioning:

fxsquared[x_] := x^2
Manipulate[Plot[fxsquared[x], {x, a, b}], {a, 1, 5}, {b, 1, 5}]

I want to also show a point on the plot as a function of a and b. I’ve read through the documentation on Prolog and Point and this is what I’ve tried:

fxsquared[x_] := x^2
\[Xi] := (a + b)/2
Manipulate[
 Plot[fxsquared[x], {x, a, b}, 
  Prolog -> {Red, PointSize[0.02], Point[{\[Xi], fxsquared[\[Xi]]}]}, 
  PlotRange -> {{0, 5}, {0, 25}}], {a, 1, 5}, {b, 1, 5}]

This lets me manipulate the fxsquared plot, but Xi shows as a fixed point that doesn’t change as I change the values of a and b.
Can you give me any guidance on how to do this? Again, many thanks for the help. I’m learning …

4

Hi Tom,

ClearAll@ξ
ξ[a_, b_] := (a + b)/2

Manipulate[Plot[fxsquared[x], {x, a, b},
  Epilog -> {Red, PointSize[0.02], Point[{ξ[a, b], fxsquared[ξ[a, b]]}]},
  PlotRange -> {{0, 5}, {0, 25}}],
 {a, 1, 5}, {b, 1.01, 5}]

9296plot.png
9296plot.png505×429 7.97 KB

5

That’s perfect! Thank you so much!