💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# (a) Find the vertical and horizontal asymptotes.(b) Find the intervals of increase or decrease.(c) Find the local maximum and minimum values.(d) Find the intervals of concavity and the inflection points.(e) Use the information from parts $(a) - (d)$ to sketch the graph of $f$.$f(x) = \frac{x^2 - 4}{x^2 + 4}$

## a) no vertical asymptote, horizontal asymptote $y=1$b) decreasing: $(-\infty, 0) \quad$ increasing: $(0, \infty)$c) local min: $(0,-1)$d) Intervals of concavity: $x < -\frac{2 \sqrt{3}}{3}$ and $x > \frac{2 \sqrt{3}}{3},$ concave down, $-\frac{2 \sqrt{3}}{3} <$$x < \frac{2 \sqrt{3}}{3},$ concave up. Inflection points at $x=\pm \frac{2 \sqrt{3}}{3}$e) SEE GRAPH

Derivatives

Differentiation

Volume

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

Derivatives

Differentiation

Volume

Lectures

Join Bootcamp