Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 7: Exploring Derivatives of Exponential Functions. (a) (Part 2 ) Show the graph of the function m(x) = .5(3x) and the derivative function m(x). What is the formula for d dx (.5(3x))? How can you confirm this using Desmos? (b) (Part 3 ) Explain the steps you used to find the function P (x) to model the price of gas in the first 6 months of 2022. What does your function predict for April 2022 (month 3)? How does this compare to the source data? (c) (Part 4b) Explain how to find a formula for P (x), evaluate this derivative for April, and explain in words what this represents. (d) EXTRA CREDIT: (Part 7) What is Euler's constant, e? Explain what is special about the derivative of the function f (x) = ex, and how you know this