1. Use limit definition to find f'(2) for the function, f(a) = 3x2 - 4x + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging $ dollars per scone is (s) = -20s* + 150s - 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 () of your choice and it's derivative, f'(a ) and explain the changes that happened. For example, if or = a is where f () has an extreme value (max or min) then what happened to f'(a) atax = a. Explain the following: . If f () is increasing or decreasing in an interval then what happens to f'(a) in those intervals? . Is f'(ar) above or below the x-axis, 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 (x) at a == a. Find f(a) and a. (1 + h)2/3 - 1 D lim 1-+0 (2 + h)' - 16 ii) lim h + h 5. Use derivative rules to find the derivative of h(x) = 3f(x) - 29(2) -x f(x) + 83. Show steps for full credit. 6. Find the values of a at which the graph of f(a) = 4a2 - 3x + 2 has a tangent line parallel to the line y = 2x + 3. Show detailed work for full credit. 7. Find the equation of a line tangent to the graph of f(x ) = cota at a = #/4. Show all steps to receive full credit. 8. Find the derivative of f (x) = 2tanx - 3seca. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): of(x) = if(x) = r'lnx