Question

The total cost C(x) associated with the production of x units of an item is given by $C\left(x\right)=0.05x^3-0.02x^2+30x+5000$. 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.

Answer 1

Since it is Given that marginal Cost is the Instantaneous rate of change of total cost means $\Rightarrow \frac{dC}{dx}$

$\Rightarrow \frac{dC}{dx}=3\times 0.05\times x^2-2\times 0.02\times x+30=0.15x^2+0.04x+30$

Given in the Question, Marginal Costs of $3$ units is to be calculated

so, $x=3$

$\Rightarrow MarginalCost=1.35-0.12+30=31.23$