Homework Answers
15)
16)
at x=-1 , f(x) is decreasing so f '(-1) is negative ,f(x) is
concave up so f ''(-1) is positive
at x=2 , f(x) has local maximum so f '(2) =0 ,f(x) is concave down
so f ''(2) is negative
PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT
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15. Sketch the graph of a function fwith the stated properties. The function fis decreasing on th...
(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...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the m...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
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)...
Sketch a graph on the right side of the problem of a single function that has these properties. 5) (a) defined fo...
Sketch a graph on the right side of the problem of a single function that has these properties. 5) (a) defined for all real numbers (b) increasing on (-3,-1) and (2, oo) (c) f '(x) < 0 on (-00-3) and (-1,2) (d)f"x)>0 on (0, 00) (e) concave down on (-oo, -3), (-3, o) 6) (a) defined for all real numbers (b) increasing on (-3, 3) (c) decreasing on (, -3) and (3, ) (d) fix) <0 on (0, (e) f(x)>...
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)...
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where...
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. X +3 f(x) = x²-x-12 On what interval(s) is fincreasing and on what interval(s) is f decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The...
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...
> Derivatives and the shape of a graph 4- For the following exercises, determine a. intervals...
> Derivatives and the shape of a graph 4- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down, and d. the inflection points off 226. f(x)= x4 - 6x3 228. f(x)= x + x2-r3 5- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down,...
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x...
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
11. Find the intervals of increasing, decreasing concavity, and sketch the graph for the function f(x)...
11. Find the intervals of increasing, decreasing concavity, and sketch the graph for the function f(x) = 2x3 - 3x2 - 1. Label all important points. Increasing: Decreasing: (2, 3 Concave Up: 1346, og Concave Down: (-, 31)
(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...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
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)...
Sketch a graph on the right side of the problem of a single function that has these properties. 5) (a) defined for all real numbers (b) increasing on (-3,-1) and (2, oo) (c) f '(x) < 0 on (-00-3) and (-1,2) (d)f"x)>0 on (0, 00) (e) concave down on (-oo, -3), (-3, o) 6) (a) defined for all real numbers (b) increasing on (-3, 3) (c) decreasing on (, -3) and (3, ) (d) fix) <0 on (0, (e) f(x)>...
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)...
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. X +3 f(x) = x²-x-12 On what interval(s) is fincreasing and on what interval(s) is f decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The...
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...
> Derivatives and the shape of a graph 4- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down, and d. the inflection points off 226. f(x)= x4 - 6x3 228. f(x)= x + x2-r3 5- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down,...
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
11. Find the intervals of increasing, decreasing concavity, and sketch the graph for the function f(x) = 2x3 - 3x2 - 1. Label all important points. Increasing: Decreasing: (2, 3 Concave Up: 1346, og Concave Down: (-, 31)
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