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Sruthi Tadepalli MATH 184 Section 921, Summer 2012 WeBWorK Assignment 4B is due : 06/10/2013 at 08:00am PDT. (1 pt) (C) Use interval notation to...

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Sruthi Tadepalli MATH 184 Section 921, Summer 2012 WeBWorK Assignment 4B is due : 06/10/2013 at 08:00am PDT. 1. (1 pt) For the function f given above, determine whether the fol- lowing conditions are true. Input T if the condition is ture, otherwise input F . (a) f 0 ( x ) < 0 if 0 < x < 2; (b) f 0 ( x ) > 0 if x > 2; (c) f 00 ( x ) < 0 if 0 x < 1; (d) f 00 ( x ) > 0 if 1 < x < 4. (e) f 00 ( x ) < 0 if x > 4; (f) Two in±ection points of f ( x ) are, the smaller one is x = and the other is x = (Hint: Your answers should be integers.) Answer(s) submitted: T T T T T 1 5 (score 0.857142865657806) 2. (1 pt) Suppose that f ( x )= 4 x p 4 x 2 + 4 (A) Find all critical values of f . If there are no critical values, enter None . If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f ( x ) is increas- ing. Increasing: (C) Use interval notation to indicate where f ( x ) is decreasing. Decreasing: (D) Find the x -coordinates of all local maxima of f . If there are no local maxima, enter None . If there are more than one, enter them separated by commas. Local maxima at x = (E) Find the x -coordinates of all local minima of f . If there are no local minima, enter None . If there are more than one, enter them separated by commas. Local minima at x = (F) Use interval notation to indicate where f ( x ) is concave up. Concave up: (G) Use interval notation to indicate where f ( x ) is concave down. Concave down: (H) Find all in±ection points of f . If there are no in±ection points, enter None . If there are more than one, enter them sep- arated by commas. In±ection point(s) at x = Answer(s) submitted: None (-inf,inf) {} None None (0,inf) (-inf,0) 0 (correct) 3. (1 pt) Suppose that f ( x )= ln ( 9 x 2 + 2 ) . (A) List all critical numbers of f . If there are no critical val- ues, enter ’NONE’. Critical numbers = (B) Use interval notation to indicate where f ( x ) is increas- ing. Note: Use ’INF’ for , ’-INF’ for - , and use ’U’ for the union symbol. Increasing: 1
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(C) Use interval notation to indicate where f ( x ) is decreas- ing. Decreasing: (D) List the x -coordinates of all local maxima of f . If there are no local maxima, enter ’NONE’. x values of local maxima = (E) List the x -coordinates of all local minima of f . If there are no local minima, enter ’NONE’. x values of local minima = (F) Use interval notation to indicate where f ( x ) is concave up. Concave up: (G) Use interval notation to indicate where f ( x ) is concave down. Concave down: (H) List the x values of all in±ection points of f . If there are no in±ection points, enter ’NONE’. x values of in±ection points = Answer(s) submitted: 0 (0,inf) (-inf,0) None 0 ((-sqrt(2/9)),(sqrt(2/9))) (-inf,-sqrt(2)/3)U(sqrt(2)/3,+infinity) (-sqrt(2/9)),(sqrt(2/9)) (correct) 4. (1 pt) Suppose that f ( x )= x 1 / 3 ( x + 3 ) 2 / 3 (A) Find all critical values of f . If there are no critical values, enter None . If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f ( x ) is increasing. Note: When using interval notation in WeBWorK, you use I for , -I for - , and U for the union symbol. If there are no values that satisfy the required condition, then enter ”” without the quotation marks. Increasing: (C) Use interval notation to indicate where f ( x ) is decreasing. Decreasing: (D) Find the x -coordinates of all local maxima of f . If there are no local maxima, enter None . If there are more than one, enter them separated by commas. Local maxima at x = (E) Find the x -coordinates of all local minima of f . If there are no local minima, enter None . If there are more than one, enter them separated by commas. Local minima at x = (F) Use interval notation to indicate where f ( x ) is concave up. Concave up: (G) Use interval notation to indicate where f ( x ) is concave down. Concave down: (H) Find all in±ection points of f . If there are no in±ection points, enter None . If there are more than one, enter them sep- arated by commas. In±ection point(s) at x = Answer(s) submitted: None (-1,inf) (-inf,-1) -3 None {} {} -3,0 (score 0.125) 5. (1 pt) Suppose that a rectangle has an area of 66 square meters. Express the perimeter P as a function of the length x of one of the sides. P ( x ) = Answer(s) submitted: (2x)+(132/x) (correct) 6. (1 pt) At what value(s) of x on the curve y = 5 + 90 x 3 - 3 x 5 does the tangent line have the largest slope? Answer (separate by commas): x = Answer(s) submitted: -3,3 (correct) 7. (1 pt) The cost of producing x units of a product is given by C ( x )= 500 + 90 x - 90ln ( x ) , x 1 . Find the minimum average cost. Minimum Average Cost = Answer(s) submitted: (500/(eˆ(59/9)))+90-((90ln(eˆ(59/9)))/(eˆ(59/9))) (correct) 2
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Solution 1:
a) True(T)
b) True(T)
c) True(T)
d) True(T)
e) True(T)
f) i) 1 ii) 4
Solution 4:
a) X=-1
Hence critical point -1
b) There are two more points where the derivative does not exist -3 and...

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