Question

?(?)=4?^3/?^?, ?∈(−∞,∞)

a. Find ?′(?), and show how to use the First Derivative Test to find the intervals of increasing/decreasing, as well as the locations of any local maximums and/or minimums.

b.Find ?′′(?), and show how to use the Concavity Test to find the intervals of concave up and concave down, as well as the locations of any inflection points.

c.Make a list of all local extrema and inflection points, given as (?,?)coordinates(leave x-values exact, in terms of ?; round y-values to the nearest tenth, as needed).

e. Find the end behavior and locations of any horizontal asymptotes by finding: lim?→ +∞?(?) ??? lim?→−∞ ?(?)

HINT: At least one of the above limits should require the use of L’Hopital’s Rule.

HINT: For −∞, remember you can replace −∞with +∞and replace all of the x’s with negative x’s, and then find the limit.

Answer 1