2. [17 Points] DETAILS SESSCALCZ 3.3.002. MY NOTES PRACTICE ANOTHER Consider the equation below. f(x) = 4x3 + 9x2 54x + 1 (a) Find the intervals on which f is increasing. (Enter your answer using interval notation.) Find the interval on which fis decreasmg. (Enter your answer using interval notation.) (b) Find the local minimum and maXimum values of f. local minimum value local maximum value I I (c) Find the inflection point, (x, y) = ( I ) Find the interval on which fis concave up. (Enter your answer using interval notation.) Find the interval on which fis concave down. (Enter your answer using interval notation.) Need Help? _ 3. [12 Points] DETAILS SESSCALCZ 3.5.002.MI. MY NOTES PRACTICE ANOTHER Find two numbers whose difference is 100 and whose product Is a minimum. (smaller number) (larger number) Need Help? @ 4. [-12 Points] DETAILS SESSCALCZ 3.5.007.MI. MY NOTES PRACTICE ANOTHER Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible, (If both values are the same number, enter it into both blanks.) in (smaller value) m (larger value) Need Help? @ 5. [0\" Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 3.5.011.MI. MY NOTES PRACTICE ANOTHER If 10,800 :m2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 3.456.000 x cm3 Need Help? @ This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Consider the equation below. f(x) = 2x3 + 3x2 - 36x Exercise (a) Find the interval on which f is increasing. Find the interval on which fis decreasing. Click here to begin! Exercise (b) Find the local minimum and maximum values of f. Part 1 of 2 The function f(x) changes from increasing to decreasing at x = -3. Therefore, f(-3) = is ---Select--- c . Submit Skip (you cannot come back) Exercise (c) Find the inflection point. Find the interval on which fis concave up. Find the interval on which fis concave down. Click here to begin!Find the inection point. Find the interval on which 1' is concave up. Find the interval on which fis concave down. We have f'(X) = 6x2 + 6X 36, so f\"(x) = (x, rm) = (l ) (Submit) C Skip (you cannot come been) , which equals 0 when This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Consider the equation below. f(x) = 2x3 + 3x2 - 36x Exercise (a) Find the interval on which f is increasing. Find the interval on which f is decreasing. Part 1 of 6 For f(x) = 2x3 + 3x2 - 36x, we have f' ( x ) = This factors into (x + ( x - 2 ). Submit Skip (you cannot come back) Exercise (b) Find the local minimum and maximum values of f. Click here to begin! Exercise (c) Find the inflection point. Find the interval on which fis concave up. Find the interval on which fis concave down. Click here to begin