# Calculus Question and Second Derivative Test

Hello everyone.

Please solve the question with required details.

Consider the function f

(

x

) =

1. State the domain, range, and all intercepts (if any) of f(x). Check f(x) for symmetry about the axes and the origin, and state if the graph of the function is symmetric about any of those.

2. Find the limits at infinity of f(x) (limits of f(x) as x and as x

∞). Identify all asymptotes of the graph of f(x), if any.

3. Identify the open intervals of the domain where the graph of f(x) is increasing, decreasing, or constant. Use the first derivative test to identify any relative extrema of f(x).

4. Find the second derivative, f(x), and find the values of x for which f(x) = 0 or f(x) is undefined.

5. Use the second derivative test to identify any extrema of f(x).

6. Identify any open intervals in the domain where the graph of f(x) is concave up or down. Identify all inflection points, if any.

7. Sketch a detailed graph of f(x) using the above information. (You will have to embed or attach an image or photo to your post to answer this question.)