I’m confused by the difference between using f’(x) and f”(x) to find the minima and maxima of a curve

Imagine you have an object moving through time, like a car on the road. The distance that car travels=xThe speed of that object=f’(x)This is because speed is defined as the the rate of change of distance (speed=distance/time), so this is used to find the gradient of a graph, as the gradient is the measure of the change in value of a quantity. Therefore, for a curve the maxima or minima have a gradient that is equal to zero (since the graph is neither going up or down). This can help you find the points on a graph at which a maxima or minima can occur.Now, in this case f”(x) is the rate of change in speed of the car- which is also known as the acceleration. By differentiating f’(x) again to get f”(x), you can tell if the point is a minima or maxima:if it is greater than 0, then it’s a minima.if it is less than 0, then it’s a maxima.

Answered by Xorsheed Z. Maths tutor

2164 Views

See similar Maths 11 Plus tutors

Related Maths 11 Plus answers

All answers ▸

Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job?


Write these fractions from smallest to largest 1/4 , 2/3, 1/2, 2/6


How do I find 28% of 160?


fifty two thousand, seven hundred, and twenty four people went to a concert. Write this in numbers and round it to the nearest thousand.


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