The equation of a curve is x(y^2)=x^2 +1 . Using the differential, find the coordinates of the stationary point of the curve.

Firstly we need to use product rule to find the dy/dx of the left hand side (LHS). Using implicit differentiation, we know the differential of y^2 is 2y(dy/dx). Then use to product rule to obtain the dy/dy of LHS to be 2xy(dy/dx). The right hand side, we can treat as a normal differential therefore it is 2x. We can then rearrange the equation so that (dy/dx) is the subject. Now, we need to find the stationary point and to do that, we must set the differential equal to zero and rearrange to get either x or y on its own. I suggest trying to isolate y since it makes the next part a little easier. After rearranging, you should get y=root2x so then we can substitute root2x into the original equation to get the x coordinate. This is 1. To obtain the y coordinate, simply sub 1 into our equation for y and we get +/- root2.

Answered by Grace C. Maths tutor

5749 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A sequence is defined as: U(n+1) = 1/U(n) where U(1)=2/3. Find the sum from r=(1-100) for U(r)


Let p(x) =30x^3 - 7x^2 -7x + 2. Prove that (2x+1) is a factor of p(x).


Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.


How do polar coordinate systems work?


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