'I. Use limit definition to find f'(2) for the function, f(g;) = 31:2 _ 43; + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging 5 dollars per scone is P(s) = _2032 + 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(1r) of your choice and it's derivative, f'(a:) 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'(:1:) at :1: = a. Explain the following: 0 If f(1r) is increasing or decreasing in an interval then what happens to f'(33) in those intervaIS? ' l3f'(:1:) above or below the x-axis, 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 :1: = (1. Find ag) and a. 2/3 _ hrO h 4 ii) lim (2 + h) - 16 h)0 h 5. Use derivative rules to find the derivative of M5\") = 3f(;1;) ._ 29(3) ._ 1:2f(1;) + %. Show steps for full credit. 6. Find the values of :t: at which the graph off(;1:) = 4332 u 31: + 2 has a tangent line parallel to the line y = 22: + 3. Show detailed work for full credit. 7. Find the equation of a line tangent to the graph of f(:1:) = cots: at a: = 7r/4. Show all steps to receive full credit. 8. Find the derivative of f(93) = 211mm - 33ecz. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): Mac) = ii) f(:1:) = :czlna