Maximum and Minimum Values Inside Triangle

[Chas3down]

Homework Statement

Find the absolute maximum and minimum values of f(x,y) = y^2+x^2 -4x + 11 on the set D where D is the closed triangular region with vertices (8,0),(0,4) , and (0,-4) .

Homework Equations

The Attempt at a Solution

[/B]
fx = 2x - 4
fy = 2y

Critical point = (2,0)

The boundary of the triangle can be expressed in 3 lines, L1,L2, and L3. Find expressions for these lines.

L1 : x=0 y[-4,4]
L2 : y=-1/2x + 4 x[0,8]
L3 : y=1/2x - 4 x[0,8]

I checked the above, it is ALL correct.

Along L1, f can be expressed by the one variable function:
f = f(_,y) = ______
Along L2, f can be expressed by the one variable function:
f = f(x,_) = ______
Along L3, f can be expressed by the one variable function:
f = f(x,_) = ______

I don't know what to put in the blanks above

 

[Mark44]

Homework Statement

Find the absolute maximum and minimum values of f(x,y) = y^2+x^2 -4x + 11 on the set D where D is the closed triangular region with vertices (8,0),(0,4) , and (0,-4) .

Homework Equations

The Attempt at a Solution

[/B]
fx = 2x - 4
fy = 2y

Critical point = (2,0)

The boundary of the triangle can be expressed in 3 lines, L1,L2, and L3. Find expressions for these lines.

L1 : x=0 y[-4,4]
L2 : y=-1/2x + 4 x[0,8]
L3 : y=1/2x - 4 x[0,8]

I checked the above, it is ALL correct.

Along L1, f can be expressed by the one variable function:
f = f(_,y) = ______

What's the x value along this vertical line?

Along L2, f can be expressed by the one variable function:
f = f(x,_) = ______

Given an x-value, how do you find the y value? You have the formula above.

Along L3, f can be expressed by the one variable function:
f = f(x,_) = ______

Given an x-value, how do you find the y value? You have the formula above

I don't know what to put in the blanks above

 

[mfb]

Just plug in the formulas for x you have for the individual lines.

 

[Chas3down]

Thanks, solved!