This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = 8x + 8y + 4z; 4x2 + 4y2 + 4z2 = 36

The extreme max value is "" and min value is "".

According to the question,

let,

By using Lagrange multipliers,

→ ...(equation 1)

∴

then,

→

As we know,

→            

By substituting the values, we get

→

→                

→                                  

∴ x = 2, y = 2, z = 1

then,

→ (Extreme max value)

and,

∴ x = -2, y = -2, z = -1

then,

→ (min value)

Thus the above answer is correct.

Learn more about Lagrange multipliers here:

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step-by-step explanation:

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