Mathematics

Problem

Let

x>0

and consider the expression

S = x + \dfrac{16}{x}

. a. (i) Rewrite

S

so that each term is explicitly shown as a function of

x

. b. (ii) Show that

S

attains a minimum value as

x

varies over all positive real numbers. c. (iii) Determine the minimum value of

S

and the corresponding value of

x