Question

Consider the function $f(x, y) = 25x^4 + 25y^4 + 100xy + 124$. a) Find the first partial derivatives of $f(x, y)$. $\frac{\partial f}{\partial x} = 100(x^3 + y)$, $\frac{\partial f}{\partial y} = 100(x + y^3)$. b) Find the coordinates of the critical points of $f(x, y)$. Where there is more than one critical point, you should enter your answer in ascending values of the x coordinate, so $x_1 < x_2 < x_3$. You should also enter your answer as a simplified fraction. $(x_1, y_1) = (-1, 1)$, $(x_2, y_2) = (0, 0)$, $(x_3, y_3) = (1, -1)$.

          Consider the function $f(x, y) = 25x^4 + 25y^4 + 100xy + 124$.

a) Find the first partial derivatives of $f(x, y)$.
$\frac{\partial f}{\partial x} = 100(x^3 + y)$,
$\frac{\partial f}{\partial y} = 100(x + y^3)$.
b) Find the coordinates of the critical points of $f(x, y)$.
Where there is more than one critical point, you should enter your answer in ascending values of the x coordinate, so $x_1 < x_2 < x_3$. You should also enter your answer as a simplified fraction.
$(x_1, y_1) = (-1, 1)$,
$(x_2, y_2) = (0, 0)$,
$(x_3, y_3) = (1, -1)$.

$Consider the function f(x, y) = 25x^4 + 25y^4 + 100xy + 124. a) Find the first partial derivatives of f(x, y). (∂ f)/(∂ x) = 100(x^3 + y), (∂ f)/(∂ y) = 100(x + y^3). b) Find the coordinates of the critical points of f(x, y). Where there is more than one critical point, you should enter your answer in ascending values of the x coordinate, so x1 < x2 < x3. You should also enter your answer as a simplified fraction. (x1, y1) = (-1, 1), (x2, y2) = (0, 0), (x3, y3) = (1, -1).$

Added by Leah O.

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