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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the weight of the object inside the box!

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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