Given a quadratic equation, how do I find the coordinates of the stationary point?

Example curve: y = x2 + 4x + 5The first step is to differentiate the equation to give us the gradient at a general point. As a quadratic equation is an example of a polynomial, the solution is as follows:dy/dx = 2x2-1 + 14x1-1 + 0*5 = 2x + 4Since we know that stationary points are defined as points where the tangent line is horizontal (i.e. that the gradient is zero), the next step is simply to equate our previous equation with 0, and rearrange. This gives us x = -2. The final step step is to plug our value of x back into the original equation, to give us the corresponding y value, and hence the complete result: (-2, 1)

Answered by Daniel G. Maths tutor

4530 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Take the 2nd derivative of 2e^(2x) with respect to x.


A particle, P, moves along the x-axis. At time t seconds, t > 0, the displacement, is given by x=1/2t^2(t ^2−2t+1).


How do I integrate ∫ xcos^2(x) dx ?


express 9^(3x+1) in the form 3^(ax+b)


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