How do you use derivatives to categorise stationary points?

When investigating graphs, you will often be asked to pick out features of the graph; stationary points being the most popular. You will need to know that a stationary point on f(x) can be found by solving the following equation: f'(x)=0.Once you have found the stationary points, you will need to find the second derivative of the graph, also known as f''(x). By finding the values of f''(x) at the x-coordinates where stationary points exist, you can categorise the stationary points.If f''(x) > 0, then the stationary point is a minimum point.If f''(x) < 0, then the stationary point is a maximum point.If f''(x) = 0, then the stationary point is a point of inflection.

Related Further Mathematics GCSE answers

All answers ▸

Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.


Find the solution of 3^{4x} = 9^{(x-1)/2}.


Use the factor theorem to show that (x-1) is a factor of x^3 - 3x^2 -13x + 15


The curve C has equation f(x) = 4(x^1.5) + 48/(x^0.5) - 8^0.5 for x > 0. (a) Find the exact coordinates of the stationary point of C. (b) Determine whether the stationary point is a maximum or minimum.


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