textbook-theory · English
The Geometry of Graphs
Section 3.9 from Dan Sloughter's open calculus textbook 'Difference Equations to Differential Equations', covering the geometry of function graphs using first and second derivatives. The section explains concavity (concave up/down), inflection points, and a systematic method for sketching graphs by combining information from f, f', and f'' along with asymptote analysis. Worked examples include polynomial, rational, and transcendental functions with detailed sign analysis.
calculusgraph analysisconcavityinflection points