I think if you check types (using whattype command) is possible to understand the problem with the first code.

> restart;

> pwl := x < 0, -1, x < 1, 0, 1;
                     x < 0, -1, x < 1, 0, 1
> whattype(pwl);
                            exprseq
> k := proc (x) options operator, arrow; piecewise(pwl) end proc;
x -> piecewise(pwl)
> whattype(k);
                             symbol
> k;
                               k
> whattype(k(x));
                            function
> k(x);
               piecewise(x < 0, -1, x < 1, 0, 1)

k is an operator and you need an expression for plot.

I hope it's help.

Regards.

I think if you check types (using whattype command) is possible to understand the problem with the first code.

> restart;

> pwl := x < 0, -1, x < 1, 0, 1;
                     x < 0, -1, x < 1, 0, 1
> whattype(pwl);
                            exprseq
> k := proc (x) options operator, arrow; piecewise(pwl) end proc;
x -> piecewise(pwl)
> whattype(k);
                             symbol
> k;
                               k
> whattype(k(x));
                            function
> k(x);
               piecewise(x < 0, -1, x < 1, 0, 1)

k is an operator and you need an expression for plot.

I hope it's help.

Regards.

The problem with your approach is that you have an infinite number of curves that accomplished your constraints:

f(8)=g(8) and diff(f,x)(8)=diff(g,x)(8).

With the approach I described before I get the following graph for f and g;

The problem with your approach is that you have an infinite number of curves that accomplished your constraints:

f(8)=g(8) and diff(f,x)(8)=diff(g,x)(8).

With the approach I described before I get the following graph for f and g;

What do you understand by "get a graph like" ?

I understood try to find a and b such that the "distance" between g = 0.00083*x^4-0.09375*x^2+3 and f = a*cos(b*x)+3 is a global minimum in the interval x =[-8..8]

Using a "distance" based in the L2 norm:

distance = int((f-g)²,x=-8..8)

you could try to find an answer (maybe using the optimization package).

I suggest to try with a more general f = a*cos(b*x)+c. You will get a best solution.

What do you understand by "get a graph like" ?

I understood try to find a and b such that the "distance" between g = 0.00083*x^4-0.09375*x^2+3 and f = a*cos(b*x)+3 is a global minimum in the interval x =[-8..8]

Using a "distance" based in the L2 norm:

distance = int((f-g)²,x=-8..8)

you could try to find an answer (maybe using the optimization package).

I suggest to try with a more general f = a*cos(b*x)+c. You will get a best solution.