y >0 means increasing; y <0 means decreasing on an interval. A positive tangent gradient means output rises as input rises; a negative tangent gradient means it falls. A missing input separates domain components. Method Find derivative zeros and all excluded inputs, order them, test its sign in each interval and state the intervals in the original domain. Example y=x+ 1x, y = x2-1x2 is decreasing for -1<x<0 and 0<x<1. Exam check Never join intervals across an excluded input. The sign of the function itself does not tell you whether it is increasing.

\(y^{\prime}>0\) means increasing; \(y^{\prime}<0\) means decreasing on an interval.

A positive tangent gradient means output rises as input rises; a negative tangent gradient means it falls. A missing input separates domain components.

Find derivative zeros and all excluded inputs, order them, test its sign in each interval and state the intervals in the original domain.

\(y=x+\dfrac1x,\quad y^{\prime}=\dfrac{x^2-1}{x^2}\) is decreasing for \(-1<x<0\) and \(0<x<1\).

Never join intervals across an excluded input. The sign of the function itself does not tell you whether it is increasing.

Increasing and decreasing intervals

Increasing and decreasing intervals