# Calculus

posted by .

Determine the function is concave upward and where it is concave downward
f(x)= x / (x+1)

• Calculus -

f ' (x) = ( x+1 - x)/(x+1)^2 = (x+1)^-2
f ''(x) = 2(x+1)-3
= 1/(x+1)^3

if x > -1 , f ''(x) is positive, so the curve is convace upwards
if x < -1, f ''(x) is negative, so the curve is concave downwards.

notice x ≠ -1, so there is a vertical asymptote at x + 1 = 0

• Calculus oops -

I think you dropped a minus sign on f'', so the intervals are reversed.

## Similar Questions

1. ### Calculus

Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. Determine where the function is concave up and concave down.
2. ### Calculus

Function f(x)= e^-x^2 a) Inflection Values b) Intervals on which f(x) is concave downward c) Intervals on which f(x) is concave upward.
3. ### Calculus

Determine where the function is concave upward and where it is concave downward. g(x)=-x(^2)+4x+8
4. ### Math ( calculas)

find the intervals on which the curve y=x/(x+1)^2 is concave upward or concave downward.
5. ### calculus

Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. a) Determine where the function is increasing and decreasing. b) Determine where the function is concave up and concave down. ________________________________________ I know: f′(x)=cos(x)+2sin(x) …
6. ### Calculus

3. Discuss the graph of y=x/3+2+3/x. Determine the values of x for which the graph is a. Continuous b. Rising c. Falling d. Concave upward e. Concave downward f. Has a relative maximum g. Has a relative minimum
7. ### math

Determine where the function is concave upward and where it is concave downward. g(x)=-x^2+7x+9
8. ### math

Determine where the function is concave upward and where it is concave downward. Concave upward: A. (-/infty,0) B.(-1,1) C.(0, infinity) D. (- infinity,infinity) E. (no interval) Concave downward: A.(-/infty,0) B.(-1,1) C.(0, infinity) …
9. ### Calculus

THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on which the function is concave up or concave down. I finally understand that when f'' is greater than 0 it means concave up. f(X) = 18x^2 + x^4 so I differentiate that …
10. ### Calculus

Determine the open intervals on which the graph of f(x) = -7x^2 + 8x + 1 is concave downward or concave upward. The second derivative is just -14, so I don't know what to do with that.

More Similar Questions