Find the x and y coordinates of the minimum of the following equation: y = x^2 - 14x + 55.

We can see that the quadratic function will be U-shaped, as the quadratic term is with a positive sign. Therefore, the absolute extreme of the function will be a minimum. Step 1: Differentiate to find the slope of the function. dy/dx = 2x - 14Step 2: Find where the slope equals 0. This will be the x coordinate. 2x -14 = 0 2x = 14 x = 7Step 3: Substitute x into the original equation, to get the functions value at x. y = 7^2 - (14 x 7) +55 y = 49 - 98 + 55 y = 104 - 98 y = 6Step 4: We have our coordinates: (7,6)

FD
Answered by Ferenc Dániel Z. Further Mathematics tutor

1588 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.


How many different ways are there to seat 6 people at a round table?


Find the coordinates of the minimum point of the function y=(x-5)(2x-2)


The function f is given by f(x) = SQRT(2x − 5). Work out x when f(x) = 1.2


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