Optimization & Taylor Approximation

Use derivatives to find extrema and build local approximations. Compare stationary points and boundaries, distinguish local and global maxima, and construct Taylor polynomials, geometric sums and exponential series. Prerequisites: limits, derivatives and basic integration. Challenges address constrained optima, nonattainment on open intervals, curvature-based error direction and explicit remainder bounds.

Further reading:

• Paul Dawkins: Absolute extrema
• Paul Dawkins: Taylor series
• Paul Dawkins: Series basics

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