Consider the function f(x) =x/x^2+1
(a) Find all values ofxfor which f(x) is positive or negative.Discuss the behaviour of f(x) as x gets very large (in both thepositive and negative direction).
(b) Draw a sign diagram clearly showing the values of x forwhich f(x) is increasing and decreasing. Hence find the criticalpoints off(x) and determine their nature.
(c) Draw a sign diagram clearly showing the values of x forwhich f(x) is concave up and concave down. Hence identify anypoints of inflection off(x).
(d) Sketch the graph of f(x), clearly showing all the featuresidentified above.
