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).
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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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