The typical daily energy use of a household is described by afunction f : [?12, 12] ? [0, ?). The value of f(x) is theconsumption rate at given time x. Both points x = ?12 and x = 12 ofthe domain correspond to 3am so f(12) = f(?12). It is also knownthat 9am and 9pm (x = ?6 and x = 6, respectively) are local maximaof the consumption rate. In this question we model the rate by apolynomial of degree 4 that is f(x) = a4x4 + a3x3 + a2x2 + a1x +a0and assume that the total energy consumption during the dayequals 24.
(a) Write a linear system of equations describing the followingproperties: f(12) = f(?12), [4]x = ?6, 6 are stationary points of fand the total energy consumption is 24.
