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

6757 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If the functions f and g are defined: f: x--> x/5 + 4 g : x--> 30x + 10. what is x, if fg(x) = x. ?? What would fgf(x) = x^2 be??


Functions: If f(x)=3x^2 - 4 and g(x) = x + 3, 1) Evaluate f(3), 2) Find the inverse of f(x) (f^-1(x)), 3)Find fg(x).


The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the


Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.


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