- If the Total Revenue is given by $f(x)$, the Marginal Revenue is the rate of change of total revenue and is nothing but the first order derivative of the function $\large \frac{df(x)}{dx}$

Given the total revenue $=R(x)=3x^2+36x+5$.

If the Total Revenue is given by $f(x)$, the Marginal Revenue is the rate of change of total revenue and is nothing but the first order derivative of the function $\large \frac{df(x)}{dx}$

$\Rightarrow$ Differentiating $R(x)$, we get $\large \frac{dR(x)}{dx}$$ = 6x+36$

If $x=5$, Marginal revenue $= 6 (5) + 36$

Therefore, Marginal revenue $= 30+36 = 66$.

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