Find A and B in a Piecewise Function such that it is differentiable

TehPingwin

Hello Everyone! Usually a trivial matter, first make sure it's continuous and then make sure the derivatives are the same but in this one one of the functions goes to 0 and I can't get a usable relation for A and B.

I've been googling a lot but all the examples I can find are trivial with Ax+2B etc.
Anyway, here's what I've got so far:

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romsek

MHF Helper

$f(x) = \begin{cases} (x+A) e^{x^2} &x \leq 1 \\ B \sin(\sqrt{\pi^2 x} &1 < x \end{cases}$

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TehPingwin

Did you try to enlarge it? I can see it full size no problem on my side. EDIT: I made it bigger in the post.
And it's almost correct.
It should be:

$f(x) = \begin{cases} (x+A) e^{x^2} &x \leq 1 \\ B \sin(\sqrt{\pi^2 x} &1 < x \end{cases}$

Pi is squared.

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tgeofrey

MHF Helper

TehPingwin

TehPingwin

Thank you! It turns out my derivatives were wrong and that's why I couldn't accept A=-1 but now it all makes sense.