1. ## [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.

2. 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.

3. 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?

4. 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.

5. ok, i tried doing that but now I'm stuck
the actual problem is
.where and are constants.

If is differentiable at , what are the values of and

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