Question

The total cost (in dollars) to produce x units of a burger is defined by the given function. C(x)=

ˣ²+2/3x+4 What is the marginal cost [MC=
dxdCwhen x=20?​ ]

Answer 1

To find the marginal cost, differentiate the total cost function with respect to x and substitute x=20 into the equation. The marginal cost is $40.67.

Step-by-step explanation:

To find the marginal cost, we need to calculate dC/dx and then substitute the value of x=20 into the equation.

The function to find the total cost is C(x)=x^2+2/3x+4.

To differentiate C(x) with respect to x, we use the power rule for differentiation:

1. Apply the power rule to the term x^2 to get 2x.
2. Apply the power rule to the term (2/3)x to get 2/3.
3. Since 4 is a constant, its derivative is zero.

Now we have dC/dx = 2x + 2/3.

Substituting x=20 into the equation, we have MC = dC/dx when x=20 = 2(20) + 2/3 = 40 + 2/3 = 40 2/3 = $40.67.