Page 1 of 5 MATH 1431 EMCF 4 Due 10/12 at 11:59 pm Log into CASA and access the answer sheet by clicking on the EMCF tab. Choice F is “None of the above” on all questions. 1. What is/are the point(s) of inflection for( )54x 3x 10x 1f =−+ ? A. x= 0 and x = 2 B. x = 0 and x = 1 C. x = 1 and x = 2 D. x = 2 E. x= -2 2. What is/are the point(s) of inflection for ( )=−221fxx? A. x= -1, x = 1 B. x = -1, x= 0, x= 1 C. x = 1, x= 0 D. x = 0 E. No points of inflection Questions 3-4: The graph of f “(x) (second derivative!) is given below.Page 2 of 5 3. When is the function f(x) concave down? A. () (),. .,.−∞15 and 2835 B. ( ) ( ),,−∞ ∞1 and 2 C. (1,2) D. (2.3,3.5) E. ( ) ( ),,−∞ 1 and 2 4 4. What are the points of inflection of f(x)? A. x= 1.5 , x = 2.3, x = 3.5 B. x= 1, x =2, x = 4 C. x= 2.3, x = 3.5 D. x= 1, x = 2 E. x = 2, x = 4 Questions 5-7: The graph of f ‘(x) (first derivative!) is given below.Page 3 of 5 5. When is the function f(x) decreasing? A. ( ) ( ),,−∞ ∞0 and 2 B. ( ),−∞ 1 C. (0,2) D. ( ),∞1 E. ( ),−∞ ∞ 6. When is the function f(x) concave up? A. ( )(),,−∞ ∞0 and 2 B. (),−∞ 1 C. (0,2) D. ( ),∞1 E. ( ),−∞ ∞ 7. What are the points of inflection of f(x)? A. x = 0 and x = 2 B. x = 1 C. x = 0 D. x =2 E. No points of inflectionPage 4 of 5 8. Which of the following functions is always concave up? A. ()/=13fx x B. () ()15fx x1/= − C. ( )= +42fx x x D. ( ) ( )3fx x1= − E. ()= +5f x 2x 1 For Questions 9 and 10; inspect the given graphs and investigate the choices to see which one fits the information gathered by your inspection. Think about asymptotes, holes, y-intercept, etc. This is simply testing whether you know basic properties of rational functions or not. 9. The graph of a function is given above. Which of the following can be this function? A. ( )22x 4xfxx9−=− B. ( )222x 4fxx9−=− C. ( )222x 8fxx9−=+ D. ( )224x 4xfxx9−=− E. ( )22x4fxx9−=−Page 5 of 5 10. The graph of a function is given above; the function has a hole at the point B. Which of the following can be this function? A. ( )22xxfxx4+=− B. ( )( )( )22xxfxx1x 4+=−− C. ()( )()22xxfxx1x 4+=+− D. ( )( )( )22xxfxx1x 4−=−− E. ( )( )( )22x1fxx1x
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