Find the stationary points of the function z = 3x(x+y)3 - x3 + 24x

z = 3x(x+y)3 - x3 + 24xDifferentiating partially with respect to x and with respect to y:∂z/∂x = 3(x+y)3 + 9x(x+y)2 - 3x2 + 24∂z/∂y = 9x(x+y)2At stationary points: ∂z/∂x = 0 and ∂z/∂y = 0.From ∂z/∂y = 0 we deduce: x = 0 or y = -x.We consider ∂z/∂x = 0 in each of these cases:For x = 0:3y3 + 24 = 0y = -2Hence a stationary point at (0, -2, 0)For y = -x:-3x2 + 24 = 0x = 2√2 and x = -2√2Hence stationary points at (2√2, -2√2, 32√2) and (-2√2, 2√2, -32√2)

HT
Answered by Harvey T. Further Mathematics tutor

1967 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

In statistics, what is the benefit of taking a sample survey rather than a census?


3 points lie in a plane; P1=i+2j+3k, P2=-3i+5j+2k, P3=i+2j+k. Find the Cartesian equation of the plane


Prove that "6^n + 9" is divisible by 5 for all natural numbers.


Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences