Please provide the answer in digital writing because I can't read handwritten. Thank you so much.

1. Use limit denition to nd f'(2) for the function, f(3) = 332 4.1: + 1. Show detailed work for credit. 2. A coffee shop determines that the daily prot on scones obtained by charging 3 dollars per scone is 13(3) = 20,532 + 1503 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 iE prices on scones. 3. Use Desmos to graph a cubic polynomial function, f (1') of your choice and it's derivative, rm) and explain the changes that happened. For example, if J: = a. is where f(:r:) has an extreme value (max or min) then what happened to f'(x) at 1' = (1 Explain the following: 0 lff(3:) is increasing or decreasing in an interval then what happens to 1'13) in those intervals? |Sf"(x) above or below the x-axis, and why? Then repeat with the graph a polynomial function, f (3:) 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(:t:) at J: = a. Find f(x) and a. 2/3 _ i} lim l1 + h) 1 rHo h 4 ii) lim (2+ h) 16 hvO h 5. Use derivative rules to find the derivative ofh(;;) = 3114:) _ 29(1) _ sz(g) + 5%. Show steps for full credit. 6. Find the values of: at which the graph ofx) = 4:52 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 ofx) = cats: at a: = 17/4. Show all steps to receive full credit. 8. Find the derivative of \"1] = 2mm- 3.98622. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): D= ii)f(:c) = xglnz