PLEASE USE THE TYPING SCREEN OR WORD FILE I USE A SCREEN READER thank you.

PLEASE DO SHOW ALL THE STEPS FOR ALL THE QUESTIONS.

1. Use limit definition to find f'(2) for the function, f(3;) = 31:2 _ 41: + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging 3 dollars per scone is P(s) = 2032 -+- 1503 10. The coffee shop currently charges $3.25 per scone. Find P'(3_25), 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, f(1:) of your choice and it's derivative, f'(:z:) and explain the changes that happened. For example, if :1: = a is where f(1:) has an extreme value (max or min) then what happened to f'(:1:) at a: = (1. Explain the following: - lf f(:z:) is increasing or decreasing in an interval then what happens to f'(;1:) in those intervals? . lsf'(:1:) above or below the xaxis, and why? Then repeat with the graph a polynomial function, f(1:) of degree 4 and repeat the same exercises. Show your work in full for maximum credit. 4. For the following exercises, the given limit represents the derivative of a function y = f(:):) at): = 0:. Find f(:r) and a. 2/3 _ i) lim (1 + h) 1 hbO h 4 ii) \"\"1 (2 + h) 16 1110 h 5. Use derivative rules to find the derivative of _ 2 9(3) - [1(3) _ 3f(35) _ 29(3) _ g; f(;;;) + 3L1. Show steps for full credit. 6. Find the values of :1: at which the graph off(a:) = 43:2 3:35 + 2 has a tangent line parallel to the line y = 2:): + 3. Show detailed work for full credit. 7. Find the equation of a line tangent to the graph of f(.1:) = cats: at :1: = 7r/4. Show all steps to receive full credit. 8. Find the derivative of f(:1:) = 2mm}: 333cm. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): i) HI) = s ii) f(:1:) = 1221111