A company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x (in hundreds of thousands of dollars), according to the formula given below. n(x) = -1 + 8x + 2x² – 0.3x3 (a) Find n"(2) and n"(3). n"(2) = n"(3) = Interpret the results. With $200,000 invested in R&D, the number of new products per $100,000 is increasing at a rate of new products per $100,000 per $100,000, and with $300,000 invested in R&D, it is decreasing at a rate of new products per $100,000 per $100,000. (b) Find the size of the budget that gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns). (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.