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)

Related Further Mathematics A Level answers

All answers ▸

f(x)=ln(x). Find the area underneath the curve f(x) between 1 and 2.


Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)


The finite region bounded by the x-axis, the curve with equation y = 2e^2x , the y-axis and the line x = 1 is rotated through one complete revolution about the x-axis to form a uniform solid. Show that the volume of the solid is 2π(e^2 – 1)


Find the integrating factor of the following first order ODE: dx/dt = -2tx +t.


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