1. Use limit definition to find f'(2) for the function, f($) = 332 41 + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging 8 dollars per scone is P(s) = 2()s2 + 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 $3.25, and decide whether or not the coffee shop should consider raising or lowering its prices on scones. 3. Use Desmos to graph a cubic polynomial function, f(1:) of your choice and it's derivative, f'(:1:) and explain the changes that happened. For example, if :1: = a is where f(1:) has an extreme value (max or min) then what happened to f'(z) at :1: = (1. Explain the following: U lff($) is increasing or decreasing in an interval then what happens to f'(z) in those intervals? 0 |sf'(a:) above or below the xaxis, and why? Then repeat with the graph a polynomial function, f(z) 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 :1: = (1. Find f(x) and a. 2/3 _ i) lim (l'l'hll 1H0 h 4 ii) \"m (2+ h) 16 hrO 5. Use derivative rules to find the derivative of [1(1) = 3f(g;) _ 2901;) _ Izz) + %. Show steps for full credit. 6. Find the values ofx at which the graph off(z) = 4:1;2 3g; + 2 has a tangent line parallel to the line y = 2:1: + 3. Show detailed work for full credit. 7. Find the equation of a line tangent to the graph off(1:) = cotrL' at :1: = 7r/4. Show all steps to receive full credit. 8. Find the derivative off(z) = 2tana: 339cm. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): 0 f($) = ii) f(x) = z2lm