Differential And Integral Calculus By Feliciano And Uy Chapter 4 -

This is the workhorse of calculus differentiation. Feliciano and Uy present this as a generalization applicable to any real number exponent.

Follow this Feliciano & Uy checklist:

Critical points – solve (f'(x)=0).

Increasing/Decreasing – sign of (f'(x)).

Local extrema – use 1st or 2nd derivative test.

Concavity & inflection points – sign of (f''(x)).

Plot points & sketch curve.

| Section | Typical problems | |---------|------------------| | 4.1 | Tangent & normal lines (polynomials, radicals, rationals) | | 4.2 | Increasing/decreasing intervals | | 4.3 | Relative extrema (1st derivative test) | | 4.4 | Concavity & inflection points | | 4.5 | Curve sketching (polynomials, rationals) | | 4.6 | Applied max/min (geometric, numeric, cost) | | 4.7 | Time rates (ladder, conical tank, balloon, shadow) | This is the workhorse of calculus differentiation