Problem:
Numerically, investigate the behavior of the Newton quotient of the function

f(x) = x2 + 4 x - 3

near x = 3

Visualization: Using Maple:

> f:= x -> x^2+4*x-3;

> L:=[n, 2^(-n), (f(3+2^(-n))-f(3))/2^(-n), (f(3-2^(-n))-f(3))/(-2^(-n)), (f(3+2^(-n))-f(3-2^(-n)))/(2*2^(-n))];

> for n from 0 to 10 do print(evalf(L)); od;