(Must show all work to receive credit) (Round answer to nearest It'll.)th if needed) 1.) Given the function f(x) = 3x3 6x2 + 2x + 1 nd and label any points that are relative maximums/minimums. 2.) From the graph below please let me please let me know which points (if any) produce: 0 Absolute Maxima 0 Absolute Minima 0 Relative Maximum 0 Relative Minimum 3.) Find the interval where the following function is increasingldecreasing and then the interval where the function is concave up/concave down. f(x) = ex(x 1) 4.) Determine whether Rolle's Theorem applies. If so, find the point guaranteed to exist. f(x) = x3 - x2 -5x - 3 on [-1,3] 5.) Determine whether Mean Value Theorem applies. If so, find the point guaranteed to exist. f(x) = 7 - x2on [-1,2] 6.) Determine whether Mean Value Theorem applies. If so, find the point guaranteed to exist. f(x) = 3sin(2x) on [0,z]7.) Describe the difference between Rolle's theorem and Mean Value Theorem. 8.} Find positive numbers x and V such that xy = 12 and the sum 2): + y is as small as possible. 9.} A rectangular pen is built with one side against a barn. Two hundred meters of fencing are used for the other 3 sides of the pen. What is the maximum area of the pen? 10.)A man wishes to get from an initial point on the corner of a square lake to the terminal point on the opposite corner of the lake (diagonally across). Each side to the lake is exactly 2 miles long. If he walks 4 mph and swims 2 mph what is the minimum time for the trip?