SHORT RUN COST FUNCTION TC=6Q^3-18Q^2+Q=100...FIND MC,AVC

MC= TC - TC(one less)

TC= AVC*Q

i need answer this quation

To find the marginal cost (MC) and average variable cost (AVC) from the given total cost (TC) function, we need to take the derivative of TC with respect to Q. Let's break down the steps:

Step 1: Start with the given total cost function:
TC = 6Q^3 - 18Q^2 + Q = 100

Step 2: Take the derivative of TC with respect to Q. Since TC includes multiple terms, we need to take the derivative of each term separately, using the power rule.

Derivative of 6Q^3 with respect to Q:
d(6Q^3)/dQ = 3 * 6Q^2 = 18Q^2

Derivative of -18Q^2 with respect to Q:
d(-18Q^2)/dQ = -2 * 18Q = -36Q

Derivative of Q with respect to Q:
dQ/dQ = 1

Step 3: Combine the derivatives to find the marginal cost (MC):
MC = dTC/dQ = 18Q^2 - 36Q + 1

Step 4: To find the average variable cost (AVC), we need to divide the total variable cost (TVC) by the quantity (Q).

The total variable cost (TVC) represents the cost of producing the variable inputs, which can be calculated as the difference between the total cost (TC) and the total fixed cost (TFC).

TVC = TC - fixed cost (TFC)

Since the fixed cost (TFC) is not given in the problem, we cannot determine AVC without additional information.

Therefore, the marginal cost (MC) can be calculated as 18Q^2 - 36Q + 1, but the average variable cost (AVC) cannot be determined without knowing the fixed costs.