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Q)

If the marginal cost of manufacturing a product is $C' = 3 + 0.25x$, find the total cost of function $C$ given that $C(0) = 60$.

(A) $C(x) = 3x + 0.125x^2 - 60$ (B) $C(x) = 3x + 0.125x^2 + 60$ (C) $C(x) = 3x^2 + 0.125x + 60$ (D) $C(x) = 3x^3 + 0.125x^2 + 60x+c$

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A)
Given that $C' = \large\frac{dC}{dx}$$ = 3 + 0.25x$, Rearranging and integrating, we get:
$C(x) = 3x + 0.25 \large\frac{x^2}{2}$$+k$
Given that $C(0) = 60 \rightarrow 60 = 3 \times 0 + 0.25 \large\frac{0^2}{2}$$ + k \rightarrow k = 60$
Therefore, the total cost function is given by $C(x) = 3x + 0.125x^2 + 60$
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