Consider the function f(x) =x/x^2+1 (a) Find all values ofxfor which f(x) is positive or negative....

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 the positive and negative direction).

(b) Draw a sign diagram clearly showing the values of x for which f(x) is increasing and decreasing. Hence find the critical points off(x) and determine their nature.

(c) Draw a sign diagram clearly showing the values of x for which f(x) is concave up and concave down. Hence identify any points of inflection off(x).

(d) Sketch the graph of f(x), clearly showing all the features identified above.

Expert Solution

milcah answered 2 years ago

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Consider the function f(x) =x/x^2+1 (a) Find all values ofxfor which f(x) is positive or negative....

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