- #1

Kolika28

- 146

- 28

- 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?