Find the extreme values of f subject to both constraints. (if an answer does not exist, enter dne.) f(x, y, z) = yz + xy; xy = 1, y2 + z2 = 9

Extreme values .

Step-by-step explanation:

Given information:

constraints condition:

The LaGrange's auxiliary function

On partial differentiation with respect to .

    (equation number.1)

On partial differentiation with respect to .

    (equation number.2)

On partial differentiation with respect to .

(equation number.3)

By (equation number 1)

By

On addition,

put() and()

On subtraction,

,   from here,

,from here

So we have four critical points,

Then put these value into the function

We get,

extreme values .

Hence the answer is extreme values .

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answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb