009A Sample Final 2, Problem 10

Let

$f(x)={\frac {4x}{x^{2}+1}}$

(a) Find all local maximum and local minimum values of $f,$ find all intervals where $f$ is increasing and all intervals where $f$ is decreasing.

(b) Find all inflection points of the function $f,$ find all intervals where the function $f$ is concave upward and all intervals where $f$ is concave downward.

(c) Find all horizontal asymptotes of the graph $y=f(x).$

(d) Sketch the graph of $y=f(x).$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

Return to Sample Exam