# HW 9 - mandel (tgm245) HW09 Radin (56470) 1 This print-out...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: mandel (tgm245) HW09 Radin (56470) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points If f is the function whose graph is given by 2 4 6 2 4 6 which of the following properties does f have? A. f ( x ) &gt; 0 on (2 , 4) , B. local minimum at x = 4 , C. critical point at x = 2 . 1. B and C only 2. A only 3. all of them 4. none of them 5. A and B only 6. B only 7. A and C only correct 8. C only Explanation: The given graph has a removable disconti- nuity at x = 4 and a critical point at x = 2. On the other hand, recall that f has a local maximum at a point c when f ( x ) f ( c ) for all x near c . Thus f could have a local max- imum even if the graph of f has a removable discontinuity at c ; similarly, the definition of local minimum allows the graph of f to have a local minimum at a removable disconitu- ity. So it makes sense to ask if f has a local extremum at x = 4. Inspection of the graph now shows of the three properties A. f has , B. f does not have , C. f has . 002 10.0 points If the graph of the function defined on [ 3 , 3] by f ( x ) = x 2 + ax + b has an absolute minimum at (2 , 3), deter- mine the value of f (1). 1. f (1) = 2 correct 2. f (1) = 1 3. f (1) = 4 4. f (1) = 3 5. f (1) = 0 Explanation: The absolute minimum of f on the inter- val [ 3 , 3] will occur at a critical point c in ( 3 , 3), i.e. , at a solution of f ( x ) = 2 x + a = 0 , or at at an endpoint of [ 3 , 3]. Thus, since this absolute minimum is known to occur at x = 2 in ( 3 , 3), it follows that f (2) = 0 , f (2) = 3 . These equations are enough to determine the values of a and b . Indeed, f (2) = 4 + a = 0 , mandel (tgm245) HW09 Radin (56470) 2 so a = 4, in which case f (2) = 4 8 + b = 3 , so b = 1. Consequently, f (1) = 1 + a + b = 2 . 003 10.0 points If f is a continuous function on [0 , 6] having (1) an absolute maximum at 0, (2) an absolute minimum at 2 , and (3) a local maximum at 4, which one of the following could be the graph of f ? 1. 2 4 6 2 4 x y 2. 2 4 6 2 4 x y 3. 2 4 6 2 4 x y 4. 2 4 6 2 4 x y 5. 2 4 6 2 4 x y correct 6. 2 4 6 2 4 x y Explanation: By inspection, only 2 4 6 2 4 x y mandel (tgm245) HW09 Radin (56470) 3 can be the graph of f . keywords: absolute minimum, absolute maxi- mum, local maximum, local minimum 004 10.0 points Find all the critical points of f when f ( x ) = x x 2 + 16 . 1. x = 4 , 2. x = 4 , 16 3. x = 16 , 16 4. x = 4 , 4 correct 5. x = 0 , 4 6. x = 16 , 4 Explanation: By the Quotient Rule, f ( x ) = ( x 2 + 16) 2 x 2 ( x 2 + 16) 2 = 16 x 2 ( x 2 + 16) 2 ....
View Full Document

## This note was uploaded on 11/07/2010 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

### Page1 / 10

HW 9 - mandel (tgm245) HW09 Radin (56470) 1 This print-out...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online