# Calculus Question and Second Derivative Test

Hello everyone.

Please solve the question with required details.

Consider the function **f
**Answer the following questions 1-7.

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* →

−

*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.)