The cost function of a firm is given by:
`C(x) = 300x - 10x^2 +(1)/(3)x^3` where 'x' is the output. If the marginal cost is defined as the rate of change of C(x) with respect to 'x', then find the the marginal cost when 5 units are produced.

The contentment obtained after eating X-units of a new dish at a trial function is given by the function f(x) = x^(3) + 6x^(2) + 5x +3 . If the marginal contentment is defined as the rate of change f(X) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.

The contentment obtained after eating X-units of a new dish at a trial function is given by the function f(x) = x^(3) + 6x^(2) + 5x +4 . If the marginal contentment is defined as the rate of change f(X) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) - 3x^2 +36x +5 Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

The total revenue in Rupees received from the sale of x units of a product is givne by R(x) = 3x^2 + 36 x + 5 . Find the marginal revenue, when x = 6, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x^3 - 0.02 x^2 + 30x + 5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total cost C(x) associated with product of 'x' units of an item is given by: C(x) =0.005 x^3-0.02x^2 + 30 x + 500 . Find the marginal cost when 3 units are produced.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^3 + 0.003x^2 + 15x + 4000 Find the marginal cost when 17 units are produced.

The marginal cost of a manufaacturer is given by: MC = (250x)/(sqrt(x^2+40)) where 'x' is the number of units (in thousands) prodced. If 'x' increases from 3,000 to 9,000 units, find the total increase in cost.

Verify Rolle's theorem for the function given by : f(x) = x^2 - 10x + 21 , x in [3, 7]

The total revenue received from the sale of 'x' units of a product is given by R (x) = 3x^2 + 36x + 5 . Find the marginal revenue when x = 5.