# [SOLVED] Unknown variables

• Nov 14th 2009, 02:55 PM
rawkstar
[SOLVED] Unknown variables
I need help with this problem. I want to know that I did it myself so I'm just going to describe it on here and ask how to do it.

I am given function g, which is defined in two pieces. Each piece has an unknown variable in it (k in the first piece and m in the second). It then says if g is differentiable at x=3, what are the values of k and m.

• Nov 14th 2009, 03:02 PM
skeeter
Quote:

Originally Posted by rawkstar
I need help with this problem. I want to know that I did it myself so I'm just going to describe it on here and ask how to do it.

I am given function g, which is defined in two pieces. Each piece has an unknown variable in it (k in the first piece and m in the second). It then says if g is differentiable at x=3, what are the values of k and m.

make sure the values of k and m make the function continuous at x = 3, and also make the derivative function continuous at x = 3.
• Nov 14th 2009, 03:14 PM
rawkstar
i'm not really sure what you're saying but i think this is what you mean

set the variables so that g(3) of the first piece equals g(3) of the second piece and do the same thing so that g'(3) first piece equals g'(3) of the second piece

is this what you're saying?
• Nov 14th 2009, 03:24 PM
skeeter
Quote:

Originally Posted by rawkstar
i'm not really sure what you're saying but i think this is what you mean

set the variables so that g(3) of the first piece equals g(3) of the second piece and do the same thing so that g'(3) first piece equals g'(3) of the second piece

is this what you're saying?

close enough ... btw, k and m usually represent constants.
• Nov 14th 2009, 03:33 PM
rawkstar
ok, i tried doing that but now I'm stuck
the actual problem is
http://www.mathhelpforum.com/math-he...526f0594-1.gif .where http://www.mathhelpforum.com/math-he...e8759df3-1.gif and http://www.mathhelpforum.com/math-he...d9a1501b-1.gif are constants.

If http://www.mathhelpforum.com/math-he...482c35c3-1.gif is differentiable at http://www.mathhelpforum.com/math-he...65d64c80-1.gif, what are the values of http://www.mathhelpforum.com/math-he...e8759df3-1.gif and http://www.mathhelpforum.com/math-he...d9a1501b-1.gif

I plugged in 3 for x to solve each piece and i got g(x)=2k and g(x)=3x+2
Then i solved the derivative of each piece to get g'(x)=k/2sqrt(X+1) and g'(x) equals m