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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(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3