The typical daily energy use of a household is described by a function f : [−12,...

The typical daily energy use of a household is described by a function f : [−12, 12] → [0, ∞). The value of f(x) is the consumption rate at given time x. Both points x = −12 and x = 12 of the domain correspond to 3am so f(12) = f(−12). It is also known that 9am and 9pm (x = −6 and x = 6, respectively) are local maxima of the consumption rate. In this question we model the rate by a polynomial of degree 4 that is f(x) = a4x4 + a3x3 + a2x2 + a1x + a0and assume that the total energy consumption during the day equals 24.

(a) Write a linear system of equations describing the following properties: f(12) = f(−12), [4]x = −6, 6 are stationary points of f and the total energy consumption is 24.

Expert Solution

Colby Messinger answered 1 year ago

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