Find All the Critical Points of the Function $f ( x , y ) = x y + \frac { 8 } { x ^ { 2 } } + \frac { 8 } { y ^ { 2 } }$

question 59

Short Answer

Find all the critical points of the function $f ( x , y ) = x y + \frac { 8 } { x ^ { 2 } } + \frac { 8 } { y ^ { 2 } }$ Classify these critical points as local maxima, local minima, or saddle points.

---

Definitions:

Photorespiration

A process in plant metabolism where the enzyme RuBisCO oxygenates RuBP, wasting energy and reducing photosynthetic efficiency under certain conditions.

C3

A pathway in photosynthesis where the fixation of carbon dioxide produces a three-carbon compound as the first stable product.

C4

A photosynthetic pathway that efficiently fixes carbon dioxide in plants exposed to high light intensity and temperature, found in many grasses and crops.

CAM

Crassulacean Acid Metabolism, a photosynthetic adaptation in some plants allowing them to conserve water by fixing CO2 at night.