These are the collection of some questions which i want to learn. Please answer in detail(step by step) and also include diagram or graph if needed. Please provide typed work as many times handwriting makes hard to understand.

1. Use limit definition to find f'(2) for the function, f(3:) = 3x2 43; + 1. Showr detailed work for credit. 2. A coffee shop determines that the daily prot on scones obtained by charging S dollars per scone is P03) = 2{]52 + 1505 1D. The coffee shop currently charges $3.25 per scone. Find P'(3,25). the rate of change of profit when the price is $3.25. and decide whether or not the coffee shop should consider raising or lowering its prices on scones. 3. Use Desmos to graph a cubic polynomial function. f(1') of your choice and its derivative. fit\") and explain the changes that happened. For example. ifs? = a is where f[1') has an extreme value (max or min} then what happened to ftp) at :1: = :1. Explain the following: - Iffl:1') is increasing or decreasing in an interval then what happensto ftp) in those intervals? - Isf'(a:)above or below the xaxis. and why? Then repeat with the graph a polynomial function. f(;[:) of degree 4 and repeat the same exercises. Show your work in full for maximum credit. 4. For the following exercises. the given limit represents the derivative of a function y = f(3:) ata: = .1. Find ftr) and 3.. W3 _ i} lim (1 + h) 1 \"a 2 i? 4 16 m lim L hHJ h 5. Use derivative rules to find the derivative thCE) = 3f($) _ 29613) _ $2f($) + %. Show steps for full credit. 6. Find the values ofsc at which the graph offt = 43:2 31- + 2 has a tangent line parallel to the line y = 2:1: + 3. Show detailed work forfull credit. 7'. Find the equation of a line tangent to the graph off{3,:) = Ctm at a: = 1/11. Show all steps to receive full credit. 8. Find the derivative off(:c) = Qtanx 33333:. Show all steps to receive full credit. 9. Find the derivative of the following functions {Show all the steps forfull credit}: nm) = ii) at) = lm