Graphing a function

All That Jazz

Id be really greatful if someone could help me with this question.

Find the local max and min points, points of inflection and asymptotes for the function f(x) = x/x^2+1. Draw the function on a graph.

I managed to find the different points and the asymptote but I don''t know how to draw the graph itself, it just doesn't seem to fit together from the different points I worked out. Iv tried it a few times now and I cant make sense of it. If anybody knows what the graph should look like when its drawn it would really help. Thanks!

MathsManiac

I assume you mean x/(x^2+1).

Anyway, wolfram alpha is handy for checking such things:

http://www.wolframalpha.com/input/?i=x%2F%28x%5E2%2B1%29

bnt

I've done this before in exams with a calculator that uses variables and lets you recall formulas, so that you can quickly repeat a function with different values, just by changing "x" in memory. Reduces the chance of errors if you have the technology. :cool:

In case anyone's wondering - these kinds of questions expect you to differentiate the function. - when the 1st derivative is zero, the slope is zero, and therefore that's a local minimum or maximum;
- when the 2nd derivative is zero, the rate of change of the slope is zero, so that's an inflection point: the slope is between "curving up" and "curving down".
You solve for f'(x) = 0 or f''(x) = 0 as required, which gives you the x value(s) you need.