In this problem, p and C are in dollars and x is the number of units. A monopoly has a total cost function C = 1,000 + 54x + 18x2 for its product, which has demand function p = 162 − 3x − 2x2. Find the consumer's surplus (in dollars) at the point where the monopoly has maximum profit. (Round your answer to the nearest cent.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.