How do I determine if a stationary point on a curve is the maximum or minimum?

If you are comfortable with differentiation. You can take the second derviatve of the equation of the cruve and plug in the x value of the curve. Based on this answer you can determine if it's a maximum, minimum or stationary. A maximum would have a negative value, a minimum a positive and stationary 0. If however you are not comfortable with this method and cannot memorize the different cases you can always substitute a point slightly before and after the point you're interested in. For example if you're considering x =3. You can subsitute 2.5 and 3.5 into your derivative and based on the signs draw a diagram representing the shape of the curve.

ES
Answered by Eryk S. Further Mathematics tutor

2162 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

The equation of a curve is y = x^2 - 5x. Work out dy/dx


Solve x^(-1/4) = 0.2


How do I know I can multiply two matrices and if so, how do I do it?


What is the equation of a circle with centre (3,4) and radius 4?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning