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

5126 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find a solution to sec^(2)(x)+2tan(x) = 0


Given that the binomial expansion of (1 + kx) ^ n is 1 - 6x + 30x^2 + ..., find the values of n and k.


Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.


Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2


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