Suppose that the revenue, in dollars, from the sale of x items was R(x) = 60x−0.5x^(2), and the cost, in dollars, of producing x items was C (x) = 4x + 10. Find the rate of change of profit dP/dt when 40 items are sold (x= 40) and the rate of change of units is dx/dt = 30 units per day.

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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.