A curve has equation y = x^3 - 48x. The point A on the curve has x coordinate -4. Is A a stationary point?

A stationary point indicates that the gradient at that coordinate is 0. Hence we need to find the gradient of the line, set this to 0, and then substitute our value of x. Find dy/dx. Remember the equation for the gradient of the curve y = x^3 - 48x. Differentiation involves two steps which must be performed in the following order. If they are not performed in this order you WILL get a different result. The first step is to bring the power down to the front. Followed by reducing the power by 1. These must be done in the right order. Hence, dy/dx = 3x^2 - 48. We are told in the question that x = -4 at this point on the curve. Therefore we need to substitute -4 into the equation. Gives: 3(-4)^2 - 48 = 0. Hence gradient = 0 at this point verifies that A is a stationary point.

OH
Answered by Oliver H. Maths tutor

4573 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How to be fully prepared for the exam?


Re-arrange (3x+y)/2 = x+z making x the subject.


There are 12 counters in a bag. There is an equal number of red counters, yellow counters and blue counters in the bag. There are no other counters in the bag. 3 counters are taken from the bag. Work out the probability of taking 3 red counters.


Can you solve (2x-4)(x+1)=0?


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