How do you find the critical points of the function f(x) = x / (x^2 + 4)?

1 Answer
MoominDave
Jun 1, 2018

Find those points at which the derivative of f is equal to 0

Explanation:

The critical points of a function are those points where its first derivative is 0, i.e. those points where the function reaches a maximum, a minimum, or a point of inflection.

In this case, f(x)=x/(x^2+4), so f'(x)=(4-x^2)/(x^2+4)^2 by the quotient rule (and a little combining of terms).

This equals 0 either when the denominator equals oo (which doesn't happen here for non-infinite x) or when the numerator equals 0.

So we want 4-x^2=0, which tells us the two critical points of the function: x=+-2, which equate to f(x)=+-1/4.

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