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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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# Interpolation Functions and their derivatives

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