Final answer:
The marginal cost at x=3 is 16, calculated as the derivative of the cost function C(x)=3x² -2x+3, evaluated at x=3.
Step-by-step explanation:
The marginal cost when x=3 is found by taking the derivative of the cost function C(x)=3x² −2x+3 with respect to x and then evaluating it at x=3. The derivative of the cost function C(x) represents the marginal cost function, which provides the cost of producing one additional unit of output.
To find the derivative, we apply the power rule which tells us that the derivative of xⁿ is nxⁿ⁻¹. The derivative of 3x² is 6x, and the derivative of -2x is -2. Therefore, the marginal cost function is 6x - 2. Evaluating this at x=3 gives us 6(3) - 2, which equals 16. So, the marginal cost at x=3 is 16.