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

Nov 2019
3
1
???
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:

Blatt 5-2.png
 
Last edited:

romsek

MHF Helper
Nov 2013
6,667
3,005
California
is this correct? Your picture is nearly impossible to read.

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

Clipboard01.jpg
 
Last edited:
Nov 2019
3
1
???
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.
 
Last edited:
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Nov 2019
3
1
???
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.