 #1
 142
 26
Homework Statement:

##g(x)=\left\{
\begin{array}{ll}
\frac{e^{ax+b}1}{x}, & x>0 \\
\frac{x}{2}+1, & x\leq 0 \\
\end{array}
\right.##
If possible, find the values ##a## and ##b## that make the function g(x) differentiable.
Relevant Equations:
 The derivative
So this is what I'm thinking:
After watching some YouTube videos on the subject, the first thing I do is check for continuity. So I plug in for ## x=0## and is left with ##
\frac{e^{b}1}{0}=1##. I don't think I'm doing this right given the fact that I'm left with 0 in the denominator. Afterwards I was supposed to set the derivative equal of the to expression in the function equal to eachother, but only if it was continuous¨.
But I can't have 0 in the denominator. So does that make the function discontinuous and therefor not differentiable?
After watching some YouTube videos on the subject, the first thing I do is check for continuity. So I plug in for ## x=0## and is left with ##
\frac{e^{b}1}{0}=1##. I don't think I'm doing this right given the fact that I'm left with 0 in the denominator. Afterwards I was supposed to set the derivative equal of the to expression in the function equal to eachother, but only if it was continuous¨.
But I can't have 0 in the denominator. So does that make the function discontinuous and therefor not differentiable?