Preview Activity 3.3.1.
Let \(f(x) = 2 + \frac{3}{1+(x+1)^2}\text{.}\)
(a)
Determine all of the critical numbers of \(f\text{.}\)
(b)
Construct a first derivative sign chart for \(f\) and thus determine all intervals on which \(f\) is increasing or decreasing.
(c)
Does \(f\) have a global maximum? If so, why, and what is its value and where is the maximum attained? If not, explain why.
(d)
Determine \(\displaystyle \lim_{x \to \infty} f(x)\) and \(\displaystyle \lim_{x \to -\infty} f(x)\text{.}\)
(e)
(f)
Does \(f\) have a global minimum? If so, why, and what is its value and where is the minimum attained? If not, explain why.
