Consider the functio 

 

Find the Absolute and relative minima if they exist. 

Proceed as follows

1. Compute the first-order partial derivatives

2. Find the critical points

3. Compute the second-order partial derivatives

4. Use the second derivatives test to classify the critical points

5. Find the value of the function at the local extrema if they exist

6. Find the absolute maxima and minimum by evaluation of f on the boundary of D

f(x,y) = 2y +5xy- 18x2-18y 2. on D = [-5,5]x[-1,7]