I have some sort of challenge questions/ homework from one of my math classes. It's been incredibly difficult and I would appreciate any help, thanks! Can someone please explain how to find the minimum/maximum values of these kind of questions?

Let x, y and z be positive real numbers. Find the minimum value of \((x + 2y + 4z) \left( \frac{4}{x} + \frac{2}{y} + \frac{1}{z} \right).\)

For positive real numbers x, y and z, find the minimum value of \(\frac{x^3 + 5y^3 + 25z^3}{xyz}\)

Guest May 20, 2022