# Could someone please help me with this, it would mean a lot, thank you. Activity 1 (max

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Could someone please help me with this, it would mean a lot, thank you.

Activity 1 (max 25 min): A fundamental problem in crystallography is the determination of the packing fraction of a crystal lattice, which is the fraction of space occupied by the atoms in the lattice, assuming that the atoms are hard spheres. When the lattice contains exactly two different kinds of atoms, it can be shown that the packing fraction is given by the formula K(1+c'x3 ) f (x ) = (1 +x) 3 where x = - is the ratio of the radii, r and R of the two kinds of atoms in the lattice, and c and K R are positive constants. [NOTE: Although you may do the following by hand if you prefer, it's a bit messy, so it's probably best if you do the question entirely in Maple]. a) The function f(x) has exactly one critical number, find it. b) The numbers c and K and the domain of f(x) depend on the cell structure in the lattice. For ordinary rock salt: c = 1, K =- 2 70 , and the domain is the interval (V2 -1) Ex $1. 3 Find the absolute maximum and absolute minimum values of f(x) on this interval. Plot f(x) in Maple