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Folks,
How do determine whether the derivative of a quadratic interpolation function ##ax^2+bx+c## is continous/discontinous in the context of the following
We have a a true solution approximated by 2 quadratic interpolation functions ie,
The approximation function
[itex]
f_1(x)=ax^2+bx+c, g \le x \le x_1\\ f_1(x)=dx^2+ex+f, x_1 \le x \le h
[/itex]
See attached my sketch.
Would'nt ##f_1(x)=f_2(x)## and ##f'_1(x)=f'_2(x)## at ##x_1## for the approximation function to be continous?
How do determine whether the derivative of a quadratic interpolation function ##ax^2+bx+c## is continous/discontinous in the context of the following
We have a a true solution approximated by 2 quadratic interpolation functions ie,
The approximation function
[itex]
f_1(x)=ax^2+bx+c, g \le x \le x_1\\ f_1(x)=dx^2+ex+f, x_1 \le x \le h
[/itex]
See attached my sketch.
Would'nt ##f_1(x)=f_2(x)## and ##f'_1(x)=f'_2(x)## at ##x_1## for the approximation function to be continous?
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