Mathematics

Problem

The total production cost

C(x)

(in rupees) for manufacturing

x

units satisfies

C'(x)=6x-60

for

0\le x\le 20

and

C(0)=500

. At what production level is the cost minimum in this range? a)

x=15

units b)

x=10

units c)

x=0

units d)

x=5

units

Intuitive explanation

The key insight is that minimum cost occurs where the marginal cost $C'(x)$ equals zero—this is where the rate of change of cost stops decreasing and starts increasing. Since you're given the derivative directly, find where $C'(x) = 0$ , then verify it's a minimum by checking the second derivative or the sign of $C'(x)$ around that point. This tells you the production level where efficiency peaks.

Intuitive explanation

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