I would like to know the right way to do in SAGE what I am currently doing
with Mathematica in these two examples (I actually know how to do the first
one in SAGE, but probably not in the best way):
1) Finding the intersection of a generic tangent line to f(x) with f(x):
f[x_]:= x^2(x^2-1)
L[a_,x_]:=f[a]+f'[a](x-a)
Solve[L[a,x]==f[x],x]
Here the main issue for me is how use the derivative f'(x) without having
to define a new function g(x)=derivative(f(x))
2) Testing if |f(z)| < f(|z|) for various choices of f:
Pl[f_,r_]:=Plot[Abs[f[r Exp[I t]]]/f[r],{t,0,2Pi}]
Here I am mostly interested in how to write a command that uses a function
as a variable.
Thanks for any suggestions.
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