calculus
posted by money
find the interval on which the graph of f(x)=ln(x^2+1) is concave upward.

bobpursley
f'=1/(x^2+1) *2x
f"=2/(x^2+1) 4x^2/(x^2+1)^2 check that.
now, when is f" zero?
f"=0=> 2=4x^2/(x^2+1)
2x^2=x^2+1
x=+1 So pick three points, say x=2, x=0, and x=2 and see what f" is, is it positive?
Check my work, it is easy to make an error on a keyboard.
Respond to this Question
Similar Questions

Calculus
Find: (a) the interval(s) on which f is increasing, (b) the interval(s) on which f is decreasing, (c) the open interval(s) on which f is concave up, (d) the open interval(s) on which f is concave down, and (e) the Xcoordinate(s) of … 
Calculus
Find: (a) the interval(s) on which f is increasing, (b) the interval(s) on which f is decreasing, (c) the open interval(s) on which f is concave up, (d) the open interval(s) on which f is concave down, and (e) the Xcoordinate(s) of … 
Calculus
Let f be the function defined for x >or= to 0 with f(0)=5 and f', the first derivative of f, give by f'(x)=e^(x/4)sin(x^2). A) Use the graph of f' to determine whether the graph of f is concave up, concave down, or neither on the … 
AP Calculous
let f be the function defined by f(x)=3X^5 5X^3 +2 a) on what interval is f increasing? 
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 
Calculus
F(x) = x^5 ln x A) Find the interval on which f is increasing Find the interval on which f is decreasing B) Find the local minimum value of f C) find the inflection point (x,y) Find the interval in which f is concave up Find the interval … 
Calculus
For R"(x) = 15[(x1)(e^x)(e^x)] with 0 < x < 7 What interval is the graph concave and and concave down? 
calculus help
Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the intervals of increase and decrease and the intervals of concavity. f(x)= 1+(1/x)+(5/x^2)+(1/x^3) find the interval of increase. find … 
Please check my Calculus
1. Given f(x)=6/x, choose the correct statement A. The graph of f is concave upward on the interval (negative infinity, 0) B. The graph of f is concave downward on the interval (negative infinity, 0) C. The graph of f is concave upward … 
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.