Question

If the cost function C= 3x2=5x+4.What will be the value of marginalCost at x=2​

Answer 1

Answer:

7

Note:

★ If C(x) is the cost price ( or cost function ) , S(x) or R(x) is the selling price ( selling function or revenue function ) and P(x) is the profit function for x items , then ;

P(x) = S(x) - C(x) or P(x) = R(x) - C(x)

★ If P(x) is the price per item when x items are produced , then the revenue function is given as ; R(x) = x•P(x)

★ If C(x) is the cost function and R(x) is the revenue function , then –

• Marginal cost , M.C. = dC(x)/dx

• Average cost , A.C. = C(x)/x

• Marginal revenue , MR = dR(x)/dx

Solution:

• Given : C(x) = 3x² - 5x + 4
• To find : M.C. (at x = 2) = ?

Here,

The given cost function is ;

C(x) = 3x² - 5x + 4

Now,

We know that , the Marginal cost function is given by ; M.R. = dC(x)/dx

Thus,

=> M.R. = d(3x² - 5x + 4)/dx

=> M.R. = d(3x²)/dx - d(5x)/dx + d(4)/dx

=> M.R. = 3•dx²/dx - 5•dx/dx + d(4)/dx

=> M.R. = 3•(2x) - 5 + 0

=> M.R. = 6x - 5

Hence,

Marginal cost function is ;

M.R.(x) = 6x - 5

Now,

Marginal cost at x = 2 will be ;

=> M.R.(x) = 6x - 5

=> M.R.(2) = 6•2 - 5

=> M.R.(2) = 12 - 5

=> M.R.(2) = 7

Hence,

The marginal cost at x = 2 is 7 .

Answer 2

Step-by-step explanation:

Given: Cost of function $C=3x^{2}$ $-5x+4$

To find: Marginal Cost at $x=2$

For calculation of Marginal Cost function,

We know that cost of the function is $C=3x^{2}-5x+4$.

We also know that the formula for Marginal Cost is $MR= \frac{dC(x)}{dx}$

⇒ $MR= d\frac{(3x^{2} - 5x + 4)}{dx}$

⇒$d\frac{(3x^{2}) }{dx} - d\frac{(5x)}{dx} + d\frac{(4)}{dx}$

⇒ $\frac{3.dx^{2} }{dx} - \frac{5.dx}{dx} + d \frac{(4)}{dx}$

⇒$M.R. = 3.(2x) - 5 + 0$

⇒$M.R=6x-5$

For calculation of Marginal Cost at $x=2,$

⇒ $M.R.$ × $(x) = 6x - 5$

⇒ $M.R.$ × $(2) = 6$ × $2 - 5$

⇒ $M.R.$× $(2) = 12 - 5$

⇒ $M.R.$ × $(2) = 7$

The marginal cost at $x = 2$ is 7.