Hw8so - Create assignment 57321 Homework 8 Mar 29 at 11:11 pm 1 This print-out should have 25 questions Multiple-choice questions may continue on

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Unformatted text preview: Create assignment, 57321, Homework 8, Mar 29 at 11:11 pm 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC5c03b 51:04, calculus3, multiple choice, > 1 min, wording-variable. 001 A function h has graph 2- 2 2- 2 on (- 4 , 4). If f is defined on (- 4 , 4) by f ( x ) = 1 ,- 4 < x <- 3 , Z x- 3 h ( t ) dt,- 3 ≤ x < 4 , which of the following is the graph of f ? 1. 2- 2 2- 2 correct 2. 2- 2 2 4- 2 3. 2- 2 2- 2- 4 4. 2- 2 2- 2 5. 2- 2 2- 2 Explanation: Create assignment, 57321, Homework 8, Mar 29 at 11:11 pm 2 Since f (- 3) = Z- 3- 3 h ( t ) dt = 0 , two of the five graphs can be eliminated im- mediately. On the other hand, by the Fun- damental Theorem of Calculus, f ( x ) = h ( x ) on (- 3 , 4); in particular, the critical points of f occur at the x-intercepts of the graph of h . As these x-intercepts occur at- 1 , , 2, this eliminates a third graph. Thus the remain- ing two possible graphs for f both have the same critical points and to decide which one is the graph of f we can use the first derivative test because the graph of f will have a local maximum at an x-intercept of the graph of h where it changes from positive to negative values, and a local minimum at an x-intercept where h changes from negative to positive val- ues. Consequently, the graph of f must be 2- 2 2- 2 keywords: CalC5c04s 51:04, calculus3, multiple choice, > 1 min, wording-variable. 002 The graph of f is shown in the figure 2 4 6 8 10 2 4 6 2 If the function g is defined by g ( x ) = Z x 1 f ( t ) dt, for what value of x does g ( x ) have a maxi- mum? 1. x = 1 2. x = 7 3. x = 5 correct 4. x = 6 5. not enough information given 6. x = 2 . 5 Explanation: By the Fundamental theorem of calculus, if g ( x ) = Z x 1 f ( t ) dt, then g ( x ) = f ( x ). Thus the critical points of g occur at the zeros of f , i.e. , at the x- intercepts of the graph of f . To determine which of these gives a local maximum of g we use the sign chart g +- 1 5 7 for g . This shows that the maximum value of g occurs at x = 5 Create assignment, 57321, Homework 8, Mar 29 at 11:11 pm 3 since the sign of g changes from positive to negative at x = 5. keywords: FTC, integral, sign chart, maxi- mum CalC5c08a 51:04, calculus3, multiple choice, < 1 min, wording-variable. 003 If the function F is defined by F ( x ) = d dx ‡ Z x 5 4 t 3 dt · , determine the value of F (1). 1. F (1) = 40 2. F (1) = 5 3. F (1) = 20 correct 4. F (1) = 10 5. F (1) = 60 Explanation: By the Fundamental Theorem of Calculus, Z x 5 4 t 3 dt = h t 4 i x 5 = x 20 . In this case, F ( x ) = d dx ‡ x 20 · = 20 x 19 Consequently, F (1) = 20 ....
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This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.

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Hw8so - Create assignment 57321 Homework 8 Mar 29 at 11:11 pm 1 This print-out should have 25 questions Multiple-choice questions may continue on

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