PLEASE SHOW ALL WORK 1) f(x)=x/[(x^2)+1] a) find the intervals on which f is inc

Question

PLEASE SHOW ALL WORK

1) f(x)=x/[(x^2)+1]

a) find the intervals on which f is increasing or decreasing

b) find the local max and min values of f

c) find the intervals of concavity and the inflection points

2) f(x)=(e^x)/[1-(e^x)]

a) find the vertical and horizontal asymptotes

b) find the intervals ofincrease or decrease

c) find the local max and min values

d) find the intervals of concavity and theinflection points

e) use the information from parts a-d to sketch the graph of f

Explanation / Answer

?1? ?a? f(x)= x/(x^2+1) =1/(x + 1/x)? then G(x)=1/(x + 1/x); G (x) on the (0, 1) monotone decreasing - > f (x) on the (0, 1) monotone increasing; G (x) on monotone increasing (1, + up) and f (x) in (1, + up) monotone decreasing; G (x) is monotone decreasing in (1, 0) and f (x) in a monotone increasing (1, 0); G (x) on the (- up, 1) monotone increasing - > f (x) in monotone decreasing (- up, 1); ? f (x) on the (- up, + up) no discontinuities ? f (x) = x/(x ^ 2 + 1) monotonicity is as follows: f(x) on the (- up, 1) monotone decreasing; f (x) in (1, 1) monotone increasing; f (x) in (1, + up) on monotone decreasing; ?b? ?-1.?0?the min value ??1,0? the max value? ?c?inflection points are ?-1,0?and ?1,0??

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.