Problem Set - Increading, Decreasing and Concave Functions

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au
and

Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA
ram@math.wisc.edu

Last updates: 7 December 2009

Increading, Decreasing and Concave Functions

	What does it mean for a function $f\left(x\right)$ to be continuous at $x=a$? Explain how to test if a function is continuous at $x=a$.
	What does it mean for a function $f\left(x\right)$ to be differentiable at $x=a$? Explain how to test if a function is differentiable at $x=a$.
	What does ${\left.\left(df/dx\right)\right|}_{x=a}$ indicate about the graph of $y=f\left(x\right)$? Explain why this is true.

References [PLACEHOLDER]

[BG] A. Braverman and D. Gaitsgory, Crystals via the affine Grassmanian, Duke Math. J. 107 no. 3, (2001), 561-575; arXiv:math/9909077v2, MR1828302 (2002e:20083)