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!

Max & Min

  1. Mar 10, 2010 #1
    Show that the function f(x) = x^21 + x^11 + 13x does not have a local maximum or minimum.

    So f '(x) = 21x^20 + 11x^10 + 13.

    My reasoning is as follows:

    Since the exponents (10 and 20) are even, 21x^20 and 11x^10 can never be negative, and thus, summing them can never produce a negative number to make the expression 0 = 21x^20 + 11x^10 + 13 true. So there are no critical numbers, and therefore no local max or min.

    Would this be correct?
  2. jcsd
  3. Mar 10, 2010 #2
    Yes, since for stationary/critical/etc... points to exist, your function's derivative has to have points in which its value is 0. Since your function can never have 0 values, you're correct.
    The graphical interpretation is also quite neat. Try these in Mathematica, it'll all be clear in a second, and you can also use it in the case of more complicated functions:

    [tex]Plot[x^{21} + x^{11} + {13*x}, \{ x, -10, 10\\\}] [/tex]

    [tex]Plot[21*x^{20} + 11*x^{10} + 13*x, \{ x, -10, 10\\\}][/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook