Consider the function at) = + 6 on the interval [1, 6]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1, 6) such that f' (c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Consider the function f(m) = 29:3 + 3032 126m + 1. For this function there are three important open intervals: ( 00, A), (A, B), and (B, 00) where A and B are the critical numbers. Find A :1 For each of the following open intervals, tell whether x) is increasing (type in INC) or decreasing (type in Use calculus to determine where the function is decreasing. (Be sure to use calculus as you will be required to show your work on the upcoming test(s)). Suppose f (m) is some function and you want to determine the intervals were it is increasing and decreasing. You determine the derivative is f'(:n) = 3(m 2)2(m + 3). To find the critical values, you solve f'(n:) = 0 and come up with the critical values a: = 3, :L' = 2. You divide the number line up into three intervals: a: 2. On each interval, pick a test value and determine if the derivative is positive or negative, and use that to determine if the original function is increasing or decreasing. m- f ' (as) at test value Function behavior -=EIE- J Select an answer Increasing Decreasing Question Help: C Post to forum Find the maximum and minimum values of the function 9(9) = 26 4 sin(6) on the interval [0, g]