Polynomial Extreme Values Quiz
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Questions and Answers

Which of the following functions represents a polynomial with a maximum value?

  • $x^4 + y^4 - 2x^2 + 4xy - 2y^2$
  • $x^3 + 3xy^2 - 3x^2 - 3y^2 + 7$
  • $y^2 + 4xy + 3x^2 + x^3$ (correct)
  • $x^3 + y^3 - 3axy$, where $a > 0$
  • For which function should the critical points be examined to find extreme values?

  • $xy(a - x - y)$
  • $x^3 + 3xy^2 - 3x^2 - 3y^2 + 4$ (correct)
  • $2(x^2 - y^2) - x^4 + y^4$
  • $x^3 + y^3 - 63(x + y) + 12xy$
  • Which function represents the minimum value of $u = xy + \frac{a}{3}(x + y)$?

  • $xy(3a - x - y)$ (correct)
  • $x^3 + 3xy^2 - 15x^2 - 15y^2 + 72x$
  • $x^3 + y^3 - 63(x + y) + 12xy$
  • $x^3y^2(1 - x - y)$
  • Which function represents the minimum value of $x^3y^2(1 - x - y)$?

    <p>$x^3 + y^3 - 3axy$, where $a &gt; 0$</p> Signup and view all the answers

    Which function should be used to find the minimum and maximum values of $\cos(A)$?

    <p>$x^4 + y^4 - 2x^2 + 4xy - 2y^2$</p> Signup and view all the answers

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