2.4.21 Graphing Functions Using Derivatives

Condition: Given the function \ (f \): \ (f (x) = x \ tan ^{-1} (x) \). Find the functioning area \ (F \). a. Prove that \ (F^{\ Prime \ Prime} (x) = \ frac {2} {\ left (1+x^{2} \ right)^{2}} \) b. Find where the function \ (F \) graph is bent up and down, find all the singular and critical points for the \ (F \) function, and find possible absolute maximum and minimum function \ (F \). C. Find all asymptotes of the function \ (F \). D. Build a function of the \ (F \) function.