# Thread: Need help with this problem

1. ## Need help with this problem

I am stumbling across this problem and was wondering if someone can help me, i have to find for what values of c and d will be differentiable for all values of x

$

f(x)=\left\{\begin{array}{cc}cx+d,&\mbox{ if }
x\leq -1\\cx^3+x+2d, & \mbox{ if } x>-1\end{array}\right.

$

thanks in advance

2. Originally Posted by noname1
I am stumbling across this problem and was wondering if someone can help me, i have to find for what values of c and d will be differentiable for all values of x

$

f(x)=\left\{\begin{array}{cc}cx+d,&\mbox{ if }
x\leq -1\\cx^3+x+2d, & \mbox{ if } x>-1\end{array}\right.

$

thanks in advance
f(x) must be continuous ...

-c+d = -c - 1 + 2d

and f'(x) must be continuous ...

c = 3c+1