Question

Find the absolute maximum and absolute minimum z-values of h(x, y) = 3x + 4y on the circle x^2 + y^2 = 25 using Lagrange multipliers. Point(s) will be deducted if you do not check all relevant points, or if you check points that do not need to be checked.

Clearly indicate your final answers, and do not include points on the inside of the circle.

Answer #1

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Find the absolute maximum and minimum of f(x,y)= 3x+4y within
the domain x^2+y^2 less than or equal tp 2^2
Find the points on the cone z^2=x^2+y^2 that are closest to the
point (3,4,0)

The function f(x,y)=4x-4y has an absolute maximum value and
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Use Lagrange multipliers to find both the maximum and minimum of
the function f(x, y) = 3x + 4y subject to the constraint that the
point be on the circle x 2 + y 2 = 100.

The function f(x,y,z)= 4x+z^2 has an absolute maximum and
minimum values subject to the constraint of 2x^2+2y^2+3z^2=50. Use
Lagrange multipliers to find these values.

Find the maximum product of two numbers x and y subject to 3x +
4y = 3. Hint: Use Lagrange multipliers.

Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball of radius 4 centered at the origin (i.e., x^2 + y^2
+ z^2 ≤ 16). Lay out your work neatly and clearly show your
procedure.

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

Determine the absolute maximum and minimum of the function h (x)
= 3x^3−9x^2 + 5x + 2 on the interval [−1, 2]. Check the Mean Value
Theorem for the function h (x)

use Lagrange multipliers to find the maximum of F(x,y,z)=xyz
with the constraint H(x,y,z)=x^2+y^2+z^2-8=0

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