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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

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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.

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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

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