1. Use limit definition to find for the function, . Show detailed work for credit. 2.A coffee shop determines that the daily profit on scones obtained by charging dollars per scone is . The coffee shop currently charges $3.25 per scone. Find , the rate of change of profit when the price is $3.25, and decide whether or not the coffee shop should consider raising or lowering its prices on scones. 3.Use Desmos to graph a cubic polynomial function, of your choice and it's derivative, and explain the changes that happened. For example, if is where has an extreme value (max or min) then what happened to at . Explain the following:

• If is increasing or decreasing in an interval then what happens to in those intervals?
• Is above or below the x-axis, and why?

Then repeat with the graph a polynomial function, of degree 4 and repeat the same exercises.Show your work in full for maximum credit.