Find the coordinates of the stationary points of the curve 3x=y+6x+3

First, straight away from reading the question you know this question will involve differentiating the function with respect to x so immediately you want to re-write the equation in terms of y which in this case y=3x^(2)-6x-3.From the question the question the key word stationary points should be jumping out to you and from this you should know that you'll need to differentiate the re-arranged function.Doing this you get dy/dx=6x-6 and in an exam situation the bulk of the marks will be yours.To tie up this particular question you now need to find the value of x which makes 6x-6=0 since at the stationary points the rate of change (dy/dx) or the gradient is 0.From this we can see that 6x=6 and hence x=1, plugging this into the equation of the curve we find that y=-6 and therefore the stationary point is (1,-6).

JS
Answered by James S. Maths tutor

4011 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you differentiate (3x+cos(x))(2+4sin(3x))?


How would you integrate ln(x) with respect to x?


The graph with equation y= x^3 - 6x^2 + 11x - 6 intersects the x axis at 1, find the other 2 points at which the graph intersects the x axis


The second and fifth terms of a geometric series are 750 and -6 respectively. Find: (1) the common ratio; (2) the first term of the series; (3) the sum to infinity of the series


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