What is the maximum and minimum of f(x y z)?

The function itself, f ( x, y, z) = x y z f ( x, y, z) = x y z will clearly have neither minimums or maximums unless we put some restrictions on the variables. The only real restriction that we’ve got is that all the variables must be positive.

What does it mean if a function has a minimum?

This, of course, instantly means that the function does have a minimum, zero, even though this is a silly value as it also means we pretty much don’t have a box. It does however mean that we know the minimum of f ( x, y, z) f ( x, y, z) does exist.

What is the length of X and Y in fencing?

Note that since there are 5 lengths of x in this construction and 500 feet of fencing, it follows that . See the adjoining sign chart for A ‘ . x =50 ft. and y =125 ft. ,

What is an example of x + y – z = 1?

Example 16.8.2 The plane x + y − z = 1 intersects the cylinder x2 + y2 = 1 in an ellipse. Find the points on the ellipse closest to and farthest from the origin. We want the extreme values of f = √x2 + y2 + z2 subject to the constraints g = x2 + y2 = 1 and h = x + y − z = 1.

What is the difference between a = XY and 2x + 2y?

Let’s now think of it differently: the equation A = xy defines a surface, and the equation 100 = 2x + 2y defines a curve (a line, in this case) in the x – y plane. If we graph both of these in the three-dimensional coordinate system, we can phrase the problem like this: what is the highest point on the surface above the line?

How do you find the maximum and minimum point of tangency?

At some point you will see the path just touch a contour line (tangent to it), and then begin to cross contours in the opposite order—that point of tangency must be a maximum or minimum point. If we can identify all such points, we can then check them to see which gives the maximum and which the minimum value.