Consider the function f(x) = -2x3+ 27x2 - 84x + 10. For this function there are three important open intervals: (-0o, A), (A, B), and (B, co) where A and B are the critical numbers. Find A and B For each of the following open intervals, tell whether f (@ ) is increasing or decreasing. (-00, A) V Select an answer (A, B): $ Increasing (B, co): DecreasingConsider the function f(3:) = 4(:c 4)2/3. For this function there are two important open intervals: (00, A) and (A, 00) where A is a critical number. For each 0 ls, tell whether f(m) is increasing or decreasing. (00, A) J Select an answer (A: 00): Increasing Decreasing Consider the function f(a:) = $261093. For this function there are three important open intervals: (00, A), (A, B), and (B, 00) where A and B are the critical numbers. For each 0 (00, A) J Select an answer (A18): ' Increasing (320): Decreasing is, tell whether f(a:) is increasing or decreasing. Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a rectangular box, they measure the girth plus the length and multiply the result by $0.35. For a box with a square cross- section (measuring :1: inches to a side) and costing $140 to ship, the function V(a:) = 932(400 49:) gives the volume of the box (in cubic inches). Find the values of :1: that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function V(:v) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function V($) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for $140 (having square cross-section). cubic inches Consider the function at) 2 (5 Mam5. Find the critical number(s) of ts). Find the intervals over which at) is increasing or decreasing. Interval #1: _ J Select an answer Increasing Interval #2: . Decreasmg Classify the critical point of x) as a local min, a local max, or neither. The function f(m) = 82': 111(5m + 10) has a single critical number at :r: = A. Find this critical number. A=Q The function rs) = m + 2\"\" has a single critical number at a: = A. Find this critical number. A = S v' Select an answer n the interval (00, A). decreasing n the interval (A, 00). increasin , g r a: = A the function - Answer the following questions for the function f(m) = my :32 + 1 defined on the interval 4 g a: S 6. f(m) is concave down on the interval x = to x = aw) is concave up on the interval x = to x = The inflection point for this function is at x = _ The minimum for this function occurs at x = The maximum for this function occurs at x = Given f(m) = 42:3 36:1:2 + 6:1: + 15 The x-value(s) of inflection point(s) of f (3:) are a: = :] Concave Down interval is: O Concave Down interval does not exist. 0 Concave Up interval does not exist. Consider the function f(a) = 8(x - 2) . For this function there are two important intervals: (-0o, A) and (A, co) where A is a critical number. A is For each of the following intervals, tell whether f (x) is increasing or decreasing. (-00, A). Select an answer (A, 0o) V Select an answer Increasing For each Decreasing vals, tell whether f (@ ) is concave up or concave down. (-OO, (A, co): Select an answer vConsider the function at) 2 $2611\". rs) has two inflection points at x = C and x = D with C