Find All Points (X, Y) Where $f ( x , y ) = x ^ { 3 } - y ^ { 2 } - 3 x + y + 5$

question 96

Short Answer

Find all points (x, y) where $f ( x , y ) = x ^ { 3 } - y ^ { 2 } - 3 x + y + 5$ has a possible relative maximum or minimum.
Enter your answer exactly as just (a, b), (c, d) with a > c and where a, b, c, d are either integers or reduced fractions of form $\frac { e } { f }$ .

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Definitions:

Saturated Fat

A type of fat found in animal products and some plant oils, known for raising cholesterol levels and potentially increasing heart disease risk.

MyPlate

A visual guide created by the U.S. Department of Agriculture to help Americans understand and follow healthy eating patterns, consisting of portions from different food groups.

DASH Food Plan

Dietary Approaches to Stop Hypertension; a diet plan promoting the reduction of blood pressure through healthy eating, focusing on low-sodium, high-fiber foods, and a variety of nutrients.

Physical Activity

Any movement produced by the contraction of skeletal muscle that increases energy expenditure above a basal level.