1. Use limit denition to find f'(2) for the function, f(_q:) = 332 4:; + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging 5 dollars per scone is 13(5) = 2052 + 1505 10. The coffee shop currently charges $3.25 per scone. Find P'(3_25), the rate of change of prot when the price is $3.25, and decide whether or not the coffee shop should consider raising or lowering its prices on SCORES. 3. Use Desmos to graph a cubic polynomial function. f(_1:) of your choice and its derivative, f'(;1;) and explain the changes that happened. For example, ifg: = a is where f(:.':) has an extreme value (max or min) then what happened to f'(x) at x = 0;. Explain the following: - |ff(1:) is increasing or decreasing in an interval then what happens to f'(w) in those intervals? - lsf'tp) above or below the x-axis. and why? Then repeat with the graph a polynomial function, f(x) of degree 4 and repeat the same exercises. Show your work in full for maximum credit. 4. For the following exercises. the given limit represents the derivative ofa function y = f(x) at x = 0;. Find f(a:) and a. _. u+nm_1 I) hm hrD h . (2 + h)4 16 Ill hm hm h 5. Use derivative rules to find the derivative of M3) = 3f($) _ 29(1) _ 3:2}:(33) + 319. Show steps for full credit. 231 6. Find the values ofa: at which the graph 0ff(;c) = 4x2 33; + 2 has a tangent line parallel to the line y = 23 + 3. Show detailed work forfull credit. 7. Find the equation ofa line tangent to the graph afx) = cots: at ,1: = 1r/4. Show all steps to receive full credit. 8. Find the derivative off(:1:) = 233113 3sec1. Show all steps to receive full credit. 9. Find the derivative ofthe following functions (show all the steps for full credit): n= iilf(a:) = flux