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.
Somebody please help
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?
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
Im stuck here please help
wait i think i might know what i'm doing after thinking about it for a second
i found g'(3) for each piece and got k/4 and m
i then set these 2 equal to each other and got k=4m
i set both pieces of g(3) equal to each other 2k=3m+2
do i use elimination/substitution to solve?