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The DERIVATIVE F"(x) of a function f(x) is given by X f'(x)= 1 + x +...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On what intervals is f increasing? Decreasing? (b) At what values of x does f have a local maximum? Local minimum? (c) On what intervals is f concave upward? Concave downward? (d) State the x-coordinate(s) of the point(s) of inflection. (e) Assuming that f(0) = 0, sketch a graph of f. 15. y A y = f'(x) --2 0 2 6 8 x -2
QUESTION 18 Suppose you calculate the second derivative of a function to be f(x)-14x-91 and that...
QUESTION 18 Suppose you calculate the second derivative of a function to be f(x)-14x-91 and that one critical point? of the critical points is 13. Using the second derivative test, what can you say about the origin al function, f(x), at this O The function has a maximum at 13. The function is increasing for all x < 13. The function has an inflection point at x = 13. O The function has a minimum at 13 O The function...
The graphing calculator window shows the graph of a function f(x) and its derivative function f(x)....
The graphing calculator window shows the graph of a function f(x) and its derivative function f(x). Decide which is the graph of the function and which is the graph of the derivative. Which of the following methods would be helpful in distinguishing the graph of the function from the graph of its derivative? O A. Compare the x-intercepts of each line to see if a horizontal tangent line occurs at that x-value on the other line. Y2 O B. Calculate...
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as...
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
The DERIVATIVE f'(x) of a function f(x) is given by f'(x) = x²(x - 3). Find...
The DERIVATIVE f'(x) of a function f(x) is given by f'(x) = x²(x - 3). Find the intervals on which the function f(x) is DECREASING OA (-2,0) and (3,00) OB. (-0,0) and (0,3) Oc (0,3) OD. (-0,0) OE (3,0)
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.
Draw a graph to match the description given. F(x) has a positive derivative over (-0,1) and...
Draw a graph to match the description given. F(x) has a positive derivative over (-0,1) and (6,9) and a negative derivative over (1,6) and (9,00). Which of the following graphs matches the description? ОА. OB. O C. OD. @ 8
The graph of the first derivative f'(x) of function f(2), 1€ (-5,5) is shown below. Then...
The graph of the first derivative f'(x) of function f(2), 1€ (-5,5) is shown below. Then f(x) has a local minimum at (-1,1) - 2+ (0,0) (4,0) (-2,0) 2 - 2 (2,-2) Graph of f'(x) Select one: O a. None of these. O b. x = -2,0,4 only. C. 2 = 2 only. d. 2= -2,4 only. e. 2 = 0 only. Oo oo Consider a function f(x), a € (-0,00) whose first derivative is f'(2) = 1 +(22 –...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable,...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On what intervals is f increasing? Decreasing? (b) At what values of x does f have a local maximum? Local minimum? (c) On what intervals is f concave upward? Concave downward? (d) State the x-coordinate(s) of the point(s) of inflection. (e) Assuming that f(0) = 0, sketch a graph of f. 15. y A y = f'(x) --2 0 2 6 8 x -2
QUESTION 18 Suppose you calculate the second derivative of a function to be f(x)-14x-91 and that one critical point? of the critical points is 13. Using the second derivative test, what can you say about the origin al function, f(x), at this O The function has a maximum at 13. The function is increasing for all x < 13. The function has an inflection point at x = 13. O The function has a minimum at 13 O The function...
The graphing calculator window shows the graph of a function f(x) and its derivative function f(x). Decide which is the graph of the function and which is the graph of the derivative. Which of the following methods would be helpful in distinguishing the graph of the function from the graph of its derivative? O A. Compare the x-intercepts of each line to see if a horizontal tangent line occurs at that x-value on the other line. Y2 O B. Calculate...
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
The DERIVATIVE f'(x) of a function f(x) is given by f'(x) = x²(x - 3). Find the intervals on which the function f(x) is DECREASING OA (-2,0) and (3,00) OB. (-0,0) and (0,3) Oc (0,3) OD. (-0,0) OE (3,0)
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.
Draw a graph to match the description given. F(x) has a positive derivative over (-0,1) and (6,9) and a negative derivative over (1,6) and (9,00). Which of the following graphs matches the description? ОА. OB. O C. OD. @ 8
The graph of the first derivative f'(x) of function f(2), 1€ (-5,5) is shown below. Then f(x) has a local minimum at (-1,1) - 2+ (0,0) (4,0) (-2,0) 2 - 2 (2,-2) Graph of f'(x) Select one: O a. None of these. O b. x = -2,0,4 only. C. 2 = 2 only. d. 2= -2,4 only. e. 2 = 0 only. Oo oo Consider a function f(x), a € (-0,00) whose first derivative is f'(2) = 1 +(22 –...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
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