Partial Derivatives Maximum and Minimum Values

  • Thread starter vzla4u2
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  • #1
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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?
 

Answers and Replies

  • #2
fzero
Science Advisor
Homework Helper
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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.
 

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