Question

): A company manufactures fuel tanks for automobile. The total weekly cost (in dollar) of producing x tank is given by
c(x)=1000+90x-0.05x^2
Find c^' (x).
Find c^' (500) and c(500).

Answer 1

Given :  A company manufactures fuel tanks for automobile. The total weekly cost (in dollar) of producing x tank is given by c(x)=1000+90x-0.05x^2

To find :  c' (500) and c(500).

Solution:

C(x)=1000 + 90x - 0.05x²

C'(x) =   0 + 90 * 1 - 0.05 * (2x)

C'(x) =  90 - 0.1x

C(500) = 1000 + 90*500 - 0.05*(500)²

= 1000  + 45000 - 12500

= 46000 - 12500

= 33500

33500 $

C'(500) = 90 - 0.1 (500)

= 90 - 50

= 40

40 $

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