With reference to Example 2.10, confirm that the function

has maximum value when x = 2/3.

Data from Example 2.10

An open conical container is made from a sector of a circle of radius 10 cm as illustrated in Figure 2.16, with sectional angle θ (radians). The capacity C cm³ of the cone depends on θ. Find the formula for C in terms of θ and the simplest associated function that could be studied if we wish to maximize C with respect to θ.

Figure 2.16

E(x) = x(1-x), 0x1