Problem Solving Set 4

07 July 2012

1. Let f ∈ C^{1}[a, b], f(a) = 0 and suppose that λ ∈ ℝ, λ > 0

is such that

|f′(x)| ≤ λ |f(x)|

for all x ∈ [a, b]. Is it true that f(x) = 0 for all x ∈ [a, b]?

2. What is the greatest sum that cannot be paid for in 2c and 5c coins?