(a)

The cost function of commodity is .

Marginal cost function is the derivative of cost function.

Differentiate on each side with respect to .

The marginal cost function is .

Substitute in above expression.

is the rate of increase in cost for the 100 item.

(b)

Find the cost of producing 101^st item :

.

Substitute in above function. 

.

Substitute in above function.

Cost of 101^st item is .

.

From (a) .

Therefore is almost same as the cost of producing the 101^st item.

(a) .

(b) is almost same as the cost of producing the 101^st item.