Partial Derivatives Maximum and Minimum Values

[vzla4u2]

Homework Statement

Find the absolute maximum and minimum values of f on
the set D.

f(x,y) = 1+4x-5y
D is the closed triangular region with vertices (0,0) (2,0) (0,3)

Homework Equations

To find the absolute maximum and minimum values of a continuous function
on a closed, bounded set :
1. Find the values of f at the critical points of f in D.
2. Find the extreme values of f on the boundary of D.
3. The largest of the values from steps 1 and 2 is the absolute maximum value;
the smallest of these values is the absolute minimum value.

The Attempt at a Solution

So I know to find the values of f at the critical points I must take partial fx and partial fy. Which both should be 0.

But fx(x,y) = 4 and fy(x,y) = -5. How do I set those equal to 0?

 

[fzero]

As you have deduced those equations do not have solutions. That means that there are no critical points of f, so you must continue to step 2.