 #1
 133
 24
Homework Statement:

##f(x)=\left\{
\begin{array}{ll}
\frac{e^{x}1}{x}, & x>0 \\
\frac{x}{2}+1, & x\leq 0 \\
\end{array}
\right.##
a) At which intervals are f strictly increasing and at what intervals are f strictly decreasing.
b) Determine any local and global extreme values for f.
c) Determines if f has asymptotes.
Relevant Equations:
 The derivative
a) At which intervals are f strictly increasing and at what intervals are f strictly decreasing.
Should I just find the derivative of both of the functions? If so, I get that the function is increasing at the intervals (−∞,0) and (0,∞). Is this right, or can I just say that the function is increasing at the interval (−∞,∞)?
b) Determine any local and global extreme values for f.
When graphing the function I don't see any local or global extreme values. f(x) consists of a straight line and curve with where f(x)=0 is not true. The whole function is not bounded, so I can't look at the values in the endpoints. But my teacher says there are extreme values. But how so?
c) Determines if f has asymptotes.
I know there is at least one horisontal asymptote, y=0, given the first function. Because
I was told there is one oblique asymptote also. But how?
Should I just find the derivative of both of the functions? If so, I get that the function is increasing at the intervals (−∞,0) and (0,∞). Is this right, or can I just say that the function is increasing at the interval (−∞,∞)?
b) Determine any local and global extreme values for f.
When graphing the function I don't see any local or global extreme values. f(x) consists of a straight line and curve with where f(x)=0 is not true. The whole function is not bounded, so I can't look at the values in the endpoints. But my teacher says there are extreme values. But how so?
c) Determines if f has asymptotes.
I know there is at least one horisontal asymptote, y=0, given the first function. Because
I was told there is one oblique asymptote also. But how?