1. Given the known information about the derivative of a function, and the function exists everywhere. Answer the following questions. a) Identify the critical points of the function. b) Create a first derivative sign chart. c) Determine the intervals on which the function increases and decreases. d) Classify the critical points as relative maximums, relative minimums or neither. f (1) = 0 f'(3) = 0 f'(8) = 0 P(x)<0 (-00, 1), (3,8) on P(x)>0 on (1,3), (8, 0)

3 1. Find the local extremes of f (x) = x³ +2xª using the first derivative test.

Find all of the x values that belong to the local minimum, local maximum, and point of inflection of the function f.

Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function  y = f(x)  given in the figure. The x y-coordinate plane is given. There is a curve with seven points on the curve (2 unlabeled and 5 labeled) and four labeled intervals on the graph. The curve enters the window in the second quadrant, goes up and right, passes through the first unlabeled point, passes through the second unlabeled point, changes direction at point A on the positive y-axis, goes down and right, passes through the point B, changes direction at point C, goes up and right, passes through point D, changes direction at point E, goes down and right and exits the window in the first quadrant. Interval a begins at the first unlabeled point and ends at the second unlabeled point. Interval b begins at the first unlabeled…