Question

Find the absolute minimum and absolute maximum of

f(x,y)=10−3x+8y

on the closed triangular region with vertices (0,0),(8,0) and
(8,12).

List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

Answer #1

Find the absolute maximum and minimum values of
f(x,y)=2x^2+y^2-xy^2 on the triangular region shown with vertices
(0,0), (0,4) and (4,4).

Find the absolute min and max values of the function
f(x, y) =x + y− x^2y on the closed triangular region with
vertices (0,0), (3,0), and (0,3).

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

Find the absolute maximum value and the absolute minimum value
of the function f ( x , y ) = x 2 y 2 + 3 y on the set D defined as
the closed triangular region with vertices ( 0 , 0 ), ( 1 , 0 ),
and ( 1 , 1 ), that is, the set D = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y
≤ x }...

Integrate the function f over the given region
f(x,y) =xy over the triangular region with vertices (0,0) (6,0)
and(0,9)

find the absolute maximum value and absolute minimum values of
the function f(x,y)4xy^2-x^2y^2-xy^3 on the set D, where D is the
closed trianglar region in the xy-plane with certices
(0,0)(0,6)(6,)0

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)

find the absolute maximum and absolute minimum values of f on
the given closed interval
f(x)=5-x^2
[-3,1]

Find the absolute maximum and absolute minimum values of f on
the given interval. f(x) = 3x^2 − 18x + 8, [0, 8] absolute minimum
value.

(a) Find the maximum and minimum values of f(x) = 3x 3 − x on
the closed interval [0, 1] by the following steps:
i. Observe that f(x) is a polynomial, so it is continuous on the
interval [0, 1].
ii. Compute the derivative f 0 (x), and show that it is equal to
0 at x = 1 3 and x = − 1 3 .
iii. Conclude that x = 1 3 is the only critical number in...

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