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Business Calculus Quiz

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1. What is the derivative of the function $f(x) = 3x^2 - 4x + 5$?

2. What does the limit $ lim_{x o 2} rac{x^2 - 4}{x - 2}$ evaluate to?

3. If a company's revenue function is given by $R(x) = 10x - x^2$, what is the quantity $x$ that maximizes the revenue?

4. What is the integral of the function $g(x) = 2x^3 + 3x^2 - x + 1$?

5. Using exponential functions, how much would an investment of $100 grow to after 3 years at an annual interest rate of 5% compounded continuously?

6. If the function $f(x) = e^x$ is differentiated, what is the resulting function?

7. What is the base logarithm of $e$ (the natural logarithm), denoted as $ log_e$?

8. In the context of business calculus, what does the concept of 'marginal cost' refer to?

9. What is the economic interpretation of the derivative of a revenue function with respect to quantity?

10. What is the purpose of the optimization problems often encountered in business calculus?