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I have two functions $f$ and $g$ defined as:

$$f := \operatorname{Spline}(\operatorname{pointsBW}, t)$$

$$g:=x \rightarrow \frac{1}{x}\int_0^x f\;dt$$

where $f$ is a functional form for a set of data points. I am trying to find the intersection of these using Maple 15. How would I do this?

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Of course, you will have obtained pointsBW in your own way.

The two curves f and g will be equal at the points where f-g is zero.

restart:
randomize():
wx:=LinearAlgebra:-RandomVector(7,generator=0..1.0):
wy:=LinearAlgebra:-RandomVector(7,generator=0..1.0) + Vector(7,5):
pointsBW := Matrix([wx,wy]):

f:=unapply(CurveFitting:-Spline(pointsBW,t),t):
g:=x->1/x*int(f(s),s=0..x):

plot([f,g],0.0..1.0,view=5.0..6.0);
plot(f-g,0.0..1.0,view=-1.0..1.0,color=blue);

map(fnormal,Student:-Calculus1:-Roots(f(x)-g(x),x=-0.0..1.0));
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