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For each of the following functions, use analytic methods to find the absolute and local extreme values of the function on the given interval. a) f (x ) = 1+ (x +1)2 , - 25x$5 b) f ( x) = 3x - x3, - 35x53 Find all absolute and local extreme values of each of the following functions. x -1 a) f (x) = x2-x+1 by = x3 + 3x2 - 1 3 For each of the following functions, use analytic methods to find the local extrema, the intervals on which the function is increasing, the intervals on which the function is decreasing. f (x) = x4-2x2+3 4 For each of the following functions, use analytic methods to find the points of inflection, the intervals on which the function is concave up, the intervals on which the function is concave down. f (x) = 4x3 -3x2- 6x+1 5 Use analytic methods to sketch the graph L Xintercent is (3.2, 0) f (x) = 2+3x2 -x3 Copy the graphs ( 15 + + 2 " "derivatives ) and add a sketch of fix ) that passes through point ?. y = f'(x ) y = f" ( x ) At which of the five points on the graph of y = f(x) shown y = f (x) S here If (a) are y' and y" both negative? R (b) is y' negative and y" positive