Question 398844
Given a rational function {{{y = p(x)/q(x)}}}, the derivative of y is given by


{{{dy/dx = (q(x)*(d/dx)(p(x)) - p(x)*(d/dx)(q(x)))/((q(x))^2)}}} (by the quotient rule)


Set it equal to zero to find all critical points, then you can replace values of x between those critical points to determine whether the function is increasing or decreasing. Note that the function is undefined when {{{q(x) = 0}}}.