1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Extrema of function

  1. Jun 12, 2010 #1
    given this function

    f(x) = x^3+y^3+3x^2-18y^2+81y+5

    i should i find the extrema(i hope this is how it is called in english)

    so we should have gradf = 0

    3x^2+6x = 0 and 3y^2-36y+81 = 0

    here i get x = 0 or x = -2 and y = 54/9 or y = 2

    now what i want to ask is, which points will i have to take in order to check of extrema?

    it will be
    P1 = (0,54/9) and P2 = (-2,2)?
    P1 = (0,2) and P2 = (-2,54/9)?

    which one is the correct?

    Thanks in advance
  2. jcsd
  3. Jun 12, 2010 #2


    User Avatar
    Homework Helper

    i don't think your y values are correct... try subtituting them back in
    3y^2-36y+81 = 3(y^2 -12 +27) = 0

    you will need to check all of the points, either by subtituting in or a 2nd derivative check
  4. Jun 12, 2010 #3


    User Avatar
    Science Advisor

    First, as lanedance said, your solution for y is incorrect (it is easy to see that y= 2 does not satify the equation: 3(4)- 36(2)+ 81= -72+ 93= 21, not 0).

    Second, once you have correct solutions for x and y, since the two equations are completely separate, any value of x can be used with any value of y- there are four critical points.
  5. Jun 12, 2010 #4
    thanks a lot for your help :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook