How do I calculate where a function is increasing/decreasing?

This depends entirely on the gradient of the function, which is calculated as (dy/dx).

At (dy/dx)= 0, the function is neither increasing nor decreasing, since the gradient is zero. The max number of stationary points will be the same as the highest power (of the differential).

Plug in values either side of these stationary points. A positive dy/dx value means that the function is increasing, and a negative one means that the function is decreasing.

For example, say an equation has a stationary point (dy/dx = 0) at x=1. I would try values such as x = 1.1 and x= 0.9. If dy/dx is positive both sides, the function therefore is increasing at x>1 and x<1. 

SH

Related Maths A Level answers

All answers ▸

How do you form a Cartesian equation from two parametric equations?


why is the number e important?


The line AB has equation 5x+3y+3=0. The line AB is parallel to the line with equation y=mx+7 . Find the value of m.


How do you differentiate a^x?