Mathematics

Problem

For

0\le x\le 6

, the cost (in rupees) of producing

x

units of a product is modelled by

C(x)=x^{3}-6x^{2}+15x+200

. a. (a) Determine the intervals on

[0,6]

where the cost function

C

is increasing and where it is decreasing. b. (b) Find the production level(s) in

[0,6]

for which the marginal cost is zero, and interpret the economic meaning of this result. c. (c) Identify the value of

x

[0,6]

at which the cost is minimum and compute the minimum cost.