The total cost P(x) in rupees associated with a product is given by P(x)=0.4x2+2x-10. Find the marginal cost if the no. of units produced is 5

The correct option is Rs.6.

Step-by-Step Explanation:

Marginal cost represents the rate of change of total cost with respect to the number of units produced. Mathematically, it is the first derivative of the total cost function with respect to the quantity $x$.

The given total cost function is:
$P\left(x\right)=0.4x^2+2x-10$

To find the marginal cost function, we differentiate $P\left(x\right)$ with respect to $x$:
$\text{Marginal Cost (MC)}=\frac{dP}{dx}$

Applying the power rule of differentiation ($\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$), we get:
$\text{MC}=0.4·\left(2x\right)+2·\left(1\right)-0$
$\text{MC}=0.8x+2$

Now, we evaluate the marginal cost when the number of units produced, $x$, is equal to 5:
$\text{MC at}x=5:$
$\text{MC}=0.8·\left(5\right)+2$
$\text{MC}=4+2$
$\text{MC}=6$

Thus, the marginal cost when 5 units are produced is Rs.6.