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Questions and Answers
Which of the following functions represents a polynomial with a maximum value?
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?
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 $u = xy + \frac{a}{3}(x + y)$?
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 $x^3y^2(1 - x - y)$?
Which function represents the minimum value of $x^3y^2(1 - x - y)$?
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Which function should be used to find the minimum and maximum values of $\cos(A)$?
Which function should be used to find the minimum and maximum values of $\cos(A)$?
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