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Marianne Kemp Assignment HW7 Derivative Applications I due 02/23/2012 at 11:00pm MST math1210spring2012-3 1. (1 pt) Find the absolute maximum and absolute minimum values of the function f (x) = (x − 1)(x − 5)3 + 8 3. (1 pt) Answer the following questions for the function on each of the indicated intervals. Enter ’NONE’ for any absolute extrema that does not exist. f (x) = x (A) Interval = [1, 4]. Absolute maximum = p p x2 + 2x + 2 + 1 x2 + 2x + 2 defined on the interval [−7, 6]. A. B. C. D. E. Absolute minimum = (B) Interval = [1, 8]. Absolute maximum = f (x) is concave down on the region to f (x) is concave up on the region to The inflection value for this function is The minimum for this function occurs at The maximum for this function occurs at 4. (1 pt) Answer the following questions for the function Absolute minimum = f (x) = x (C) Interval = [4, 9]. Absolute maximum = p x2 + 36 defined on the interval [−6, 5]. Absolute minimum = A. B. C. D. E. 2. (1 pt) Find the absolute maximum and absolute minimum values of the function to f (x) is concave down on the region f (x) is concave up on the region to The inflection value for this function is The minimum for this function occurs at The maximum for this function occurs at f (x) = x3 − 12x2 − 27x + 4 5. (1 pt) From Rogawski ET 2e section 4.2, exercise 9. Find the positive critical point of the function f (x) = x6x+3 on each of the indicated intervals. Enter ’NONE’ for any absolute extrema that does not exist. x= (A) Interval = [−2, 0]. Absolute maximum = 6. (1 pt) From Rogawski ET 2e section 4.3, exercise 23. Find the critical point and determine if the function is increasing or decreasing on the given intervals. y = −x2 + 4x + 4 Critical point: c = The function is: ? on (−∞, c). ? on (c, ∞). Absolute minimum = (B) Interval = [1, 10]. Absolute maximum = Absolute minimum = (C) Interval = [−2, 10]. Absolute maximum = 7. (1 pt) From Rogawski ET 2e section 4.3, exercise 12. Determine the intervals on which f is increasing or decreasing, assuming the figure below is the graph of the derivative of f. Absolute minimum = 1 On Interval 2: On Interval 3: f is ? f is ? 8. (1 pt) Find all critical values for the function f (x) = x1/9 (x − 1)2 and then list them (separated by commas) in the box below. List of critical numbers: 9. (1 pt) Find all critical numbers for the function 1 f (x) = x 3 − x On Interval 1: −2 3 and then list them (separated by commas) in the box below. If there are no critical numbers, enter None . List of critical numbers: 10. (1 pt) A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 33 feet? f is ? c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 2