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(5 points) A continuous function f, defined for all x, has the following properties: 1. f is decreasing 2. f is concave up 3. f(26) = -5 4. f'(26) = - Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an...
7) [f function g is defined by g(x) = Ta'an, xa, thon g'(1) = ? (A) 1 (B) 2 (C) 3 (D)O (E) Does not exist The graph of function g is shown below. Which of the following statements about function g is true? A) Atx=b, function g is differentiable. BY Atxa, function g is continuous, but not differentiable. C) Atx=a, function g is both continuous and differentiable Function g is not differentiable at any point. E) Atx=c, function g...
Question 1 {(,y) 4 A continuous function f(x,y) is guaranteed to have an absolute minimum on the region D, where D = + O True False Question 1 {(,y) 4 A continuous function f(x,y) is guaranteed to have an absolute minimum on the region D, where D = + O True False
Sketch the graph of a continuous function on (-4,0 satisfying the given properties f')0 for x = -3 and - 2. f has an absolute maximum x 0;fhas an absolute minimum at Choose the correct graph below and has a local minimum at x-2
ty f) -1 0 2 The above diagram is a plot of a function f(x) Is f(x) continuous at 0 and why? Choose the best response below: Yes, the function is continous at x=0, as it has a two-sided limit as x approaches 0, which is equal to f(0) itself No, because the function does not have a two-sided limit as x approaches 0 No, because the function is not defined at x0. No, because the limit of the function...
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
please explain in detail 4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be the function defined by g(x) = 5 +1.f(t) dt for-1 $154. (A) Find g(4). (B) On what intervals is gincreasing? Justify your answer. (C) On the closed interval 1 s xs 4, find the absolute minimum value of g and find the...
Below is the graph of f(x), a function defined on the domain (-5,5). f(x) For each function value, decide if the value is positive, negative, zero, or undefined. a f'(-3) is positive negative zero undefined b. "(-1) is positive negative ? a. f'(-3) is positive negative zero undefined b. f "(-1) is positive negative zero undefined c. f'(1) is ? positive negative O O zero O undefined d. f"(3) is positive ã o negative o zero o o undefined e....
If f is a continuous, decreasing function on [0,10] with a critical point at (4,2), which of the following statements must be false? A f(10) is an absolute minimum off on [0, 10] B f(4) is neither a relative maximum nor a relative minimum. С f(4) does not exist D f'(4) < 0
Suppose f(x) is a given continuous function in -1,4] such that f(-1) and f(4) have different signs and consider the bisection method on f(x) using starting interval1,4]. (a) Bound the absolute error for the approximation c3o (Remember, we define co ao +bo)/2) (b) Use bisection method's bound on absolute error to determine which cn are guar- anteed to have absolute errors less than 10-9. Suppose f(x) is a given continuous function in -1,4] such that f(-1) and f(4) have different...