2

Part of ICMC 6

Problems(2)

Derivative greater than function

Source: ICMC 2023 Round 1 P2

f: \mathbb{R} \to \mathbb{R}

be a differentiable function such that

f'(x) > f(x)>0

for all real numbers

x

f(8) > 2022f(0)

.
Proposed by Ethan Tan

calculusderivativefunctioncollege contestsICMC

Tetrahedron volume at least 1

Source: ICMC 2023 Round 2 P2

Show that if the distance between opposite edges of a tetrahedron is at least

1

, then its volume is at least

\frac{1}{3}

.
Proposed by Simeon Kiflie

geometry3D geometrytetrahedronICMCcollege contests