Given that y = 16x + 1/x , find the two values of x for which dy/dx = 0

The first stage of this question involves differentiating the equation of y in terms of x given to us. In order to differentiate, we first need to write y in terms of base x (where all the terms are x to the power of n). 1/x will go to x-1. Now we can differentiate for each term in the equation, bringing the power for each value of x down and multiplying it by the coefficient of the term, and then reducing the power of x by 1. This gives an equation for dy/dx = 16 - 1/x2.
The second stage of the question involves solving the dy/dx equation to get values of x for which dy/dx = 0. By putting our equation for dy/dx = 0 and solving it for x, we will get two values for x, which is the answer the question requires. Hence, 0 = 16 - 1/x2 , giving values of x = + 0.25 and -0.25.

AK
Answered by Andrew K. Maths tutor

4826 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

find the coordinate of the maximum value of the function f(x) = 9 – (x – 2)^2


Having a rectangular parking lot with an area of 5,000 square yards that is to be fenced off on the three sides not adjacent to the highway, what is the least amount of fencing that will be needed to complete the job?


Find the turning value of the following function, stating whether the value is min or max, y = x^2 -6x + 5


Show using mathematical induction that 8^n - 1 is divisible by 7 for n=1,2,3,...


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