Question

Find:
1. f(x)= (6x^2-2)
_______
x^3

2. f(x)= (x^2-4)^1/3

A. Domain
B. Intercepts
C. Asymptotes, behaviour and check for crossing where applicable
D. Critical Number(s)
E. Interval of Increase/Decrease
F. Local Extrema
G. Concavity and Points of Inflection

Thank you!!

Answer 1

A. #1 -- all reals except where the denominator is zero
#2. all reals, since it's an odd root

B. #1 - where the numerator is zero
#2. so easy

C. #1 where the denominator is zero
#2 none

D. #1 f' = 6(1-x^2)/x^4
#2. f' = 2x/(3((x^2-4)^2/3) where is the numerator = 0?

E. See D, and check sign of f'
F. See D and check where f'=0

G #1. f" = 12(x^2-2)/x^5
#2. f" = -2(x^2+12)/(9((x^2-4)^5/3)
inflection where f"=0
concave up where f" > 0

Check your results by typing in the functions at wolframalpha.com