An ice cream factory produces g gallons of ice cream at a cost of c dollars acco

Question

An ice cream factory produces g gallons of ice cream at a cost of c dollars according to the function c=f(g). Interpret the following facts in practical terms. F(100)= 400 F'(100)=2 1/f(500)=200 Estimate the cost of producing 105 gallons of ice cream. Explain An ice cream factory produces g gallons of ice cream at a cost of c dollars according to the function c=f(g). Interpret the following facts in practical terms. F(100)= 400 F'(100)=2 1/f(500)=200 Estimate the cost of producing 105 gallons of ice cream. Explain F(100)= 400 F'(100)=2 1/f(500)=200 Estimate the cost of producing 105 gallons of ice cream. Explain

Explanation / Answer

let the equation be = ax2+bx+c

F[100] = 10000a+100b+c = 400 ...............................1

F1[100] = 2ax+b = 200a+b = 2    ..................................2

1/F[500] = 1/[250000a+500b+c] = 200

1 = 5*107a + 105b +c   ..............................................3

SOLVING EQUATIONS

a = -7.5*10-3

b = 3.5

c = 125

F[X] = -7.5*10-3x2 + 3.5x + 125

F[105] = -82.687+367.5+125

F[105] = 409.813

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