Practice question: Find f(3) if 12 fx) = x2 . 2: Solution: To evaluate f(3), we simply plug in the value of 3 for x in the expression: f17) = 32 .2 = 7. Find f'(3) f'(3) represents the taking the first derivative of the expression and evaluating at x = 3: f'(x) = (2)3 (2-1) = (2)3 f'(3) = (2)3 = 6 Question: Find f(7) if f(x) = x2 + 7: f(7) = find f'(7) f'(7) =

Q4 Identify the Types of the following Functions: C = f(Q) = Q³ – 5Q² + 14Q + 50,. AR = f(Q) = 15 – Q, .. .

C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?

In a certain store, cashiers can serve 45 customers per hour on average. If a customers arrive at the store in a given hour, then the average number of customers C waiting in line can be modeled by the function x² C(x) = 2025 - 45x where x < 45. Answer the following questions with a graphing calculator. Round your answers to integers. 1) If 40 customers arrived in the store in the past hour, there are approximately 7 2) If there are 2 customers waiting in line, approximately customers waiting in line. customers arrived in the past hour.