Homework 9 1. Consider the function / defined by f (x) = 2x - 5x + 6. a. I used our new rules for calculating derivatives to find that f"(x) is 4x - 5. Carefully explain the steps that I followed with those rules to get my formula for f(x]. b. Use the formula f"(x) = 4x - 5 to find the slope of the tangent line to the graph of / at the point (0, 6). c. Find the equation of the tangent line to the graph of / at the point (0, 6]. d. Use Desmos to graph the function / along with the tangent line to the graph at the point (0,6]. Choose appropriate ranges of x -values and y -values (with the wrench button in the upper-right comer of your Desmos window) so that you can see both the tangent line and the graph of the original function. If your line does not look like the tangent line to the graph of f at (0, 6], you should check your work to find out what went wrong! Include a copy of your graph with your homework submission. Use our new rules of differentiation to find the derivatives of the following functions. a. /(x) =05- 27 b. s[[) = -160* + 16 + 32 c g(x) 100x] - 5x + 13. In 2008, a statistics student (named Gabe McBride] was interested in prices for used Mustang cars being offered for sale on autotrader.com. He sampled 25 cars from the website and recorded the age [in years], mileage (in thousands of miles), and asking price (in thousands of dollars] for each car in his sample. Here are the first few rows from his data table. Age Miles Price 6 8.5 32 33 45 19 82 8 119 7 24.8 23 22 15 111 10 a. Write a sentence interpreting the information presented in the row of the table that starts with the number 15. Here is a scatter plot of Gabe's full data set. Prices of used Ford Mustangs 50 45 40 35 30 Asking price (thousands of dollars 25 15 10 20 40 1.20 140 160 Car mileage (thousands of miles) b. Add a straight line to the graph to model the relationship between asking price and car mileage for Ford Mustangs in this sample of cars from autotrader.com.c. Find the equation of your line. Show your work. d. Write a sentence interpreting the slope of your line in terms of the context of the study. Your sentence should mention Ford Mustangs, mileage, and price, including appropriate units. It should also include the actual slope as a number! Before you write anything, look back at the solutions for Homework 2, Quiz 1, and our first lab activity to remember how to write this kind of sentence