Question

# The total cost C(x) associated with the production of x units of an item is given by $$C(x)=0.05x^3-0.02x^2+30x+5000$$. Find the marginal cost when $$3$$ units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Solution

## Since it is Given that marginal Cost is the Instantaneous rate of change of  total cost means $$\Rightarrow \dfrac{dC}{dx}$$$$\Rightarrow \dfrac{dC}{dx}=3\times 0.05\times x^2-2\times 0.02\times x+30=0.15x^2+0.04x+30$$Given in the Question, Marginal Costs of $$3$$ units is to be calculatedso, $$x=3$$$$\Rightarrow Marginal Cost=1.35-0.12+30=31.23$$Mathematics

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