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# The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.

Toolbox:
• If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
• $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$
• Marginal cost is the rate of change of total cost w.r.t the output.
Step 1:
Since the marginal cost is the rate of change of total cost w.r.t the output.
Therefore marginal cost (MC)=$\large\frac{dc}{dx}$$(x) \qquad\qquad\qquad\qquad\qquad=\large\frac{d}{dx}$$(0.007x^3-0.003x^2+15x+4000).$
$\qquad\qquad\qquad\qquad\qquad=0.007\times 3x^2-0.003\times 2x+15$
Step 2:
When $x=17$ we have,
$\qquad\qquad\qquad\qquad\qquad=0.007\times 3(17)^2-0.003\times 2(17)+15$
$\qquad\qquad\qquad\qquad\qquad=6.069-0.102+15$
$\qquad\qquad\qquad\qquad\qquad=Rs 20.967$.