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. 

Answered by Steve H. Maths tutor

6949 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

if f(x) = 4x^2 - 16ln(x-1) - 10, find f'(x) and hence solve the equation f'(x)=0.


How do we solve a second order, homogeneous, linear differential equation?


Let y = 4t/(t^2 + 5). Find dy/dt, writing your answer in it's simplest form, and find all values of t for which dy/dt = 0


Given y = x(3x+ 5)^3. Find dy/dx.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences