Hw15-max-and-min-values: Problem 7
Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: 35 attempts.
(1 point)
Find the absolute maximum and minimum values of f(x, y) = y^2 + 2x + 1 on the set D where D is the closed triangular region with vertices (4, 0), (0, 4), and (0, 4).
Part 1: Critical Points
The critical points of f are:
Part 2: Boundary Work
The boundary of the triangle can be expressed in 3 lines. Although you need to do calculations over all of the boundaries, you will only submit your results for one of them.
Find a linear equation for the side of the boundary of the region D between (4, 0) and (0, 4).
For x in [0,4]
Along this side, f can be expressed as a function of one variable:
g(x) = f(x)
n =
List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D.
Part 3: Final Results
Make sure you do the other computations along the other boundaries before you attempt this section!
Find the function's absolute maximums and minimums and where they occur.
The absolute maximum of f is:
and it occurs at
The absolute minimum of f is:
and it occurs at
If you don't get this in 3 tries, you can see a similar example online. However, try to use this as a last resort or after you have already solved the problem. There are no See Similar Examples on the Exams.
