A surface is represented by the following multivariable function,f(x,y)=1/3x^3+y^2-2xy-6x-3y+4a)

UkusakazaL 2020-12-17 Answered

A surface is represented by the following multivariable function,
f(x,y)=13x3+y22xy6x3y+4
a) Calculate fxx,fyx,fxyandfyy
b) Calculate coordinates of stationary points.
c) Classify all stationary points.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

izboknil3
Answered 2020-12-18 Author has 99 answers

Since, we have been given a surface that is represented by the following multivariable function given below:
f(x,y)=13x3+y22xy6x3y+4 (i)
To calculate:
a) fxx,fyx,fxyandfyy
Solution fx=33x22y6
fxx=2x
fy=2y2x3
fyy=2
fxy=2
andfyx=2
b) fx=x22y6
andfy=2y2x3
fx=0x22y=6 (ii)
andfy=02y2x=3 (iii)
Adding equation (ii) and (iii), we have:x22x=9
Solving for x, we have:
x=b±b24ac2ax=2±4+362x=2±102x=1±10
Since, 2y2x=32y=2x+3y=2x+32=2(1±10)+32=2±210+32
y=12(5±210)
So, stationary points are:
(110,52102),(1+10,52102),(110,5+2102),(1+10,5+2102)
c) (1+10,5+2102) is minimal and (110,52102) is a saddle point.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions