Convex functions
Exercises
Correction
Correction
| A) Convex functions --- definition and slope characterization | |
|---|---|
| 1) Establishing convexity from the chord definition | Ex 1 Ex 2 Ex 3 |
| 2) Using the slope characterization | Ex 4 Ex 5 Ex 6 |
| 3) Applying Jensen's inequality | Ex 7 Ex 8 Ex 9 |
| B) Convex differentiable functions | |
| 4) Showing convexity from \(f''\) | Ex 10 Ex 11 Ex 12 |
| 5) Bounding a numerical expression by convexity | Ex 13 Ex 14 Ex 15 |
| 6) Studying tangent position | Ex 16 Ex 17 Ex 18 |
| C) Inflection points | |
| 7) Finding inflection points | Ex 19 Ex 20 Ex 21 |
| 8) Sketching curves using \(f''\) | Ex 22 Ex 23 Ex 24 |
| 9) Counterexamples to over-strong sufficient conditions | Ex 25 Ex 26 Ex 27 |