Complicated Curve Sketch and Derivative Computation (Calc I)

[ShangMing]

Homework Statement

Homework Equations

Fundamental theorem of calculus.

The Attempt at a Solution

For the first problem, I'm completely lost. I've only worked with slant asymptotes for polynomials so finding the domain, range and intercepts is as far as I've gotten.

I'm not too great at absolute value functions either, so when I take the derivative, do I need to use two cases for positive and negative x when I'm finding intervals of increase/decrease, concavity, etc?

For the second question, I have absolutely no idea where to even begin.

Thanks PF

 

[micromass]

You don't need to know anything about slant asymptotes to answer this question. All they're asking you is to calculate two limits:

$$m=\lim_{x\rightarrow \infty}{\frac{f(x)}{x}}$$

and once you've calculates that, you need to calculate

$$\lim_{x\rightarrow \infty}{f(x)-mx}$$


And don't worry about the absolute value. You take the limit to positive infinity. This means that your x will become very large, and in particular it will become larger then -2. This means that |x+2| becomes positive. So you can drop the absolute value signs.