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Exercise 1. Sketch the graph of the following function et2 f(x) = In 1+ 1 1+...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 -...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 - 2 Moreover, f'(0) = 0 and f(1) = 0. (a) Find the function f(x). (b) Draw a graph of f(x). Indicate all asymptotes (if any), local maxima and minima, inflection points, intervals where f(x) is increasing, and intervals where f(x) is concave upward.
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection Show asymptotes with dashed lines and give their equations. Label all important points on the graph. a. f(x) is defined for all real numbers 2x b. f(x) = -1 2 c. f'(x) - d. f(2)...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection Show asymptotes with dashed lines and give their equations. Label all important points on the graph. -1 2 a. f(x) is defined for all real numbers 2x b. f'(x) = c. f"(x) = (x-1)...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 1 a f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1) d. f(2)= 2 e...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 2x X-1 2. a. f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1)2...
Sketch the curve of f(x) Sketch the curve f(x) = x -1. a. What is the...
Sketch the curve of f(x)
Sketch the curve f(x) = x -1. a. What is the domain of the function? b. Find the r and y intercepts. • y-intercept is • 2-intercept(s) is/are (if there are more than one r intercept then separate your answers with a comma.) c. Is f(x) even, odd, or neither? 1. find f(-x) = 2. Does f( - x) = f(x)? 2 3. Does f(-x) = -f(x)? 2 4. f(x) is Select an answer V...
Use the derivative f'(x) = (x - 1)(x + 1)(x + 4) to determine the local...
Use the derivative f'(x) = (x - 1)(x + 1)(x + 4) to determine the local maxima and minima off and the intervals of increase and decrease. Sketch a possible graph off (f is not unique) The local maximum/maxima is/are at x = (Use a comma to separate answers as needed.) The local minimum/minima is/are at x = (Use a comma to separate answers as needed.) The open interval(s) of increase is(are) (Type your answer in interval notation. Use a...
For the function f(x) = -**-4x find the following, and use it to graph the function....
For the function f(x) = -**-4x find the following, and use it to graph the function. Find: a) (2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e) 4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determi...
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
Sketch the logarithmic function. Label three points that lie on the graph, and determine the domain...
Sketch the logarithmic function. Label three points that lie on the graph, and determine the domain and the equation of any vertical asymptotes f(x) = -log, X la-1 Use the graphing tool to graph the function. ua- Click to enlarge -10 B- 545 er- graph Determine the domain of f(x). The domain of f(x)is (Type your answer in interval notation.) Determine the equation of any vertical asymptotes Select the correct choice below and, if necessary, fill in the answer box...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 - 2 Moreover, f'(0) = 0 and f(1) = 0. (a) Find the function f(x). (b) Draw a graph of f(x). Indicate all asymptotes (if any), local maxima and minima, inflection points, intervals where f(x) is increasing, and intervals where f(x) is concave upward.
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection Show asymptotes with dashed lines and give their equations. Label all important points on the graph. a. f(x) is defined for all real numbers 2x b. f(x) = -1 2 c. f'(x) - d. f(2)...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection Show asymptotes with dashed lines and give their equations. Label all important points on the graph. -1 2 a. f(x) is defined for all real numbers 2x b. f'(x) = c. f"(x) = (x-1)...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 1 a f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1) d. f(2)= 2 e...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is decreasing, increasing, concave up, and concave down. List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 2x X-1 2. a. f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1)2...
Sketch the curve of f(x)
Sketch the curve f(x) = x -1. a. What is the domain of the function? b. Find the r and y intercepts. • y-intercept is • 2-intercept(s) is/are (if there are more than one r intercept then separate your answers with a comma.) c. Is f(x) even, odd, or neither? 1. find f(-x) = 2. Does f( - x) = f(x)? 2 3. Does f(-x) = -f(x)? 2 4. f(x) is Select an answer V...
Use the derivative f'(x) = (x - 1)(x + 1)(x + 4) to determine the local maxima and minima off and the intervals of increase and decrease. Sketch a possible graph off (f is not unique) The local maximum/maxima is/are at x = (Use a comma to separate answers as needed.) The local minimum/minima is/are at x = (Use a comma to separate answers as needed.) The open interval(s) of increase is(are) (Type your answer in interval notation. Use a...
For the function f(x) = -**-4x find the following, and use it to graph the function. Find: a) (2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e) 4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
Sketch the logarithmic function. Label three points that lie on the graph, and determine the domain and the equation of any vertical asymptotes f(x) = -log, X la-1 Use the graphing tool to graph the function. ua- Click to enlarge -10 B- 545 er- graph Determine the domain of f(x). The domain of f(x)is (Type your answer in interval notation.) Determine the equation of any vertical asymptotes Select the correct choice below and, if necessary, fill in the answer box...
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