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MATH 142 Calculus for Business

   

Added on  2020-05-16

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Running head: MATH 142 CALCULUS FOR BUSINESSMATH 142 CALCULUS FOR BUSINESS[Author Name(s), First M. Last, Omit Titles and Degrees][Institutional Affiliation(s)]

2MATH 142 CALCULUS FOR BUSINESSFrom the given situation C(x) is the total cost of producing x units of a product hence the marginal cost is defined as the rate of change of c(x) with respect to xMarginal Cost, MC=dCdx and Average Cost function is c(x) =C/xa)The marginal cost function is found by differentiating both sides of the equation with respect to xC(x) = 0.08x2 + 2Marginal Cost, MC=dCdx=ddx(0.08x2+2)=0.08ddx(x2)+ddx(2)=0.08(2x) +0=0.16xMarginal Cost, MC=0.16xb)Average Cost function is given by c(x)=C(x)/x=0.08x2+2x=0.08x+2xDifferentiating both sides of the equation with respect to x

3MATH 142 CALCULUS FOR BUSINESSddxC(x)=ddx0.08x+2x0.08ddx(x)+2ddx(−1x2)=0.08−2x2c)Marginal Cost for x=5Marginal Cost=0.16x=01.6(5)=0.8Interpretation: When the level of production is 5 units, the total cost function is increasing at the rate of 0.8d)C(5)=n!r!(n−r)!=5!3!(5−3)!=10e)C(5).¢=n!r!(n−r)!=5!1!(5−1)!=2880f) Graph MC(x), C(x), and C(x)¢

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