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Challenge: The Taylor Series

Explore how to apply the Taylor series to approximate multivariate functions relevant to global warming factors. Learn to implement quadratic approximations around a pivot point using vector calculus concepts, enhancing your skills in mathematical modeling for optimization.

Problem statement

Imagine that scientists are trying to approximate a health score against different factors of global warming, such as the average rise in global temperature, the percentage of carbon dioxide, and any humidity.

Mathematical formulation

The scientists hypothesize that the health score is a multivariate function f:R3Rf: \R^3 \rightarrow \R ...