The cost function of ABC Inc. for the investment level x is C(x) = x^3-3x§2-9x +2 where the value of investment is from -2 to 2 units. Find the values of smallest and largest cost. Explain in detail.

Question

Please show the steps to solve this question.

Answer 1

C'(x) = 3x^2 -4x -9 = 0

x = 4/6 + or - (1/6)sqr(16+108) = about 2.52 or -1.19

C(-1.19) = -1.685 - 4.25 + 10.71 + 2 = 7.29 is a local maximum

C(2) = 8-12-18+2 = -20

C(-2) = -8-12+18+2 = 0

C(2.52) =16-19-22.7+2=-23.7 is a local minimum

x=-1.19 is a local maximum,

the cost function is cubic, which means 2 turning points, with a local minimum and local maximum. the local maximum is in the interval -2<x<2. C(x) gets increasingly large as x increases. But for the interval -2<x<2, the largest C value is when x= about -1.2. About 7.3 is the largest cost. Smallest cost is about -20 when x=2