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Given the demand for a product and the total cost function, find the maximum value of the profit. 25. Suppose the demand for a product is $12 and the total costs are C(x) = 0.3x2 + 2x + 5. What is the maximum value of the profit? Round your answer to the nearest cent. 26. Suppose the demand for a product is $15 per unit, and the total cost to produce x units is given by the function C(x) = 0.25x2 + 3x + 10. What is the maximum profit? Round your answer to the nearest cent. Assuming the demand function is linear and given the total cost function, find the number of units that maximize profit. 27. The manager of a bakery knows he can sell 60 small bags of donut holes when the price is $1.20 each. If the price is $1.50, only 48 bags are sold. The total cost function for x bags is C(x) = 0.70x + 15 dollars. Assuming a linear demand function, determine the price per bag and the number of bags sold that will maximize profit. 28. A candy store can sell 180 lollipops at 62 cents each. The store can sell 220 lollipops if the price is 54 cents each. The total cost of producing x lollipops is C(x) = 3050 - 10x + 0.04x2 cents. Find the number of lollipops that should be produced to maximize profit. Find the derivative of a logarithmic function. 29. Find the derivative of the given function. f(x) = 4x2 - In(x2) 30. Find the derivative of the given function