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1. Use limit denition to nd f'(2) for the function, f(3) = 3:52 _ 4;]: + 1. Show detailed work for credit 2. A coffee shop determines thatthe daily profit on scones obtained by chargings dollars per scone is 13(3) = 2032 + 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 its prices on scones. 3. Use Desmos to graph a cubic polynomial function, f(r) ofyour choice and its derivative. f'(2:) and explain the changes that happened. For example, if x = a is where f(:.':) has an extreme value {max or mi n] then what happened to f'(z) at x = 0;. Explain the following: I If ft!!!) is increasing or decreasing in an interval then what happens to f'(x) in those intervals? ' |Sf'(x) above or below the x-axis, and why? Then repeat with the graph a polynomial function, ftp) 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 (2:) at :1: = (.1. Find f (3:) and a. 2/3 _ i] \"m (1+ 12) 1 hM] ha ii) lim (2+ 11) 16 hIO h 5. Use derivative rules to nd the derivative ofh(g;) = 31703) _ 29(3) ... $2f(IL') + %. Show steps for full credit. 6. Find the values ofzt'. at which the graph has a line tangent off(1:) = 4x2 3;: + 2 has a tangent line parallel to the line 3; = 23:: -+ 3. Show detailed work for full credit. 7. Find the equation ofa line tangent to the graph off(;z:) = can: atx = 57/4. Show all steps to receive full credit. 8. Find the derivative of f (1:) = ung: - 333cm Show all steps to receive full credit. 9. Find the derivative of the following functions {Show all the steps for full credit): nm) = 1\" ii}f(:c) = Kim