'I. Use limit definition to find f'(2) for the function, f(g;) = 33:2 _ 43; + 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) = 2052 + 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'(g;) and explain the changes that happened. For example, ifzr = a is where f('_1:) has an extreme value (max or min) then what happened to f'(:1:) at It = (1. Explain the following: 0 If f(1') is increasing or decreasing in an interval then what happens to f'(g;) in those intervals? - Isf'(g:) 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(:1:) at :E = 0,. Find f(:1:) and a. 2/3 _ i) lim (1 + h) 1 hfo h 4 ii) lim (2 + h) 16 hfo h 5. Use derivative rules to find the derivative of h(g;) = 3f(g;) 29(93) $2f(1:) + M Show steps for full credit. 131. 6. Find the values of a: at which the graph 0ff(:1:) = 4:32 _ 31: + 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;) = cota: at :1: = 1r/4. Show all steps to receive full credit. 8. Find the derivative of f(:1:) = 2tana: 33ecx. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): 0 f(I) = 2\" ii) f(a:) = $21121