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प्रश्न
The total cost function for x units is given by C(x) = `sqrt(6x + 5) + 2500`. Show that the marginal cost decreases as the output x increases.
उत्तर
Cost function
C(x) = `sqrt(6x + 5) + 2500`
∴ Marginal Cost
M.C. = `(dC)/dx`
= `d/dx (sqrt(6x + 5) + 2500)`
= `1/(2sqrt(6x + 5)) xx 6 + 0`
= `3/sqrt(6x + 5)`
Again differentiate w.r. to ‘x’
`d/dx (M.C.) = d/dx (3/sqrt(6x + 5))`
= `3 xx ((-1)/2) (6x + 5)^(-3//2) xx 6`
= `(-9)/(6x + 5)^(3//2)`
Which is negative for all x.
Hence, the marginal cost decreases as the output x increases.
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