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Negative Leading Coefficient 1. Use the graph of f'(x) to answer: On which...
3 4. The graph of f'(x) is shown. Use the graph to answer the questions. Note:...
3 4. The graph of f'(x) is shown. Use the graph to answer the questions. Note: This is a graph of the derivative off. 4 pts For what values of x is f(x) decreasing? 2 a. b. 4 pts For what values of x is f(x) concave up? 2. 3 4 -2 C. 4 pts For what value(s) of x does f(x) have a relative minimum? -3 d. 4 pts For what value(s) of x does f(x) have an inflection...
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...
8) (8 pts total) For this problem, you will sketch a graph of f(x) = 2x4...
8) (8 pts total) For this problem, you will sketch a graph of f(x) = 2x4 + 8x3. Complete the following steps: (a) (1 pt) Determine the intercepts of the function. (b) (3 pts) Use the first derivative to find the intervals on which f increases and decreases, and the relative maximums and minimums. (c) (3 pts) Use the second derivative to find the intervals on which f is concave up and concave down, and the inflection points. (d) (1...
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
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...
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...
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all ...
question 8 has parts (A-I)
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all the critical values of fx) Note: If there are no critical values, enter NONE require answers entered in interval notation. Note, with interval notation, you can enter the empty set as (B) Use interval notation to indicate where f(z) is increasing increasing (C) Use interval notation to indicate where f(z) is decreasing Decreasing (D) List the...
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down,...
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down, locate inflection pts. Use this information to sketch the graph. (20 pts) 4x2 + 12x – f'(x) = Critical Values are: F"(x) = Possible Inflection points are: First derivative information Interval Sample point f' = + or - Show inc/dec 2nd derivative information Interval Sample point f" x f" = + or - Concavity:
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:...
Determine the intervals on which f is increasing or decreasing, assuming the figure below is the...
Determine the intervals on which f is increasing or decreasing, assuming the figure below is the graph of the derivative of f. On Interval 1: is ? < On Interval 2: f is? On Interval 3: fis ? 241 24.1 1 & -2411 If the figure below is the graph of the derivative f', answer the following: Where do the points of inflection of f occur? On which interval(s) is f concave down? 4,
3 4. The graph of f'(x) is shown. Use the graph to answer the questions. Note: This is a graph of the derivative off. 4 pts For what values of x is f(x) decreasing? 2 a. b. 4 pts For what values of x is f(x) concave up? 2. 3 4 -2 C. 4 pts For what value(s) of x does f(x) have a relative minimum? -3 d. 4 pts For what value(s) of x does f(x) have an inflection...
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...
8) (8 pts total) For this problem, you will sketch a graph of f(x) = 2x4 + 8x3. Complete the following steps: (a) (1 pt) Determine the intercepts of the function. (b) (3 pts) Use the first derivative to find the intervals on which f increases and decreases, and the relative maximums and minimums. (c) (3 pts) Use the second derivative to find the intervals on which f is concave up and concave down, and the inflection points. (d) (1...
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
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...
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...
question 8 has parts (A-I)
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all the critical values of fx) Note: If there are no critical values, enter NONE require answers entered in interval notation. Note, with interval notation, you can enter the empty set as (B) Use interval notation to indicate where f(z) is increasing increasing (C) Use interval notation to indicate where f(z) is decreasing Decreasing (D) List the...
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down, locate inflection pts. Use this information to sketch the graph. (20 pts) 4x2 + 12x – f'(x) = Critical Values are: F"(x) = Possible Inflection points are: First derivative information Interval Sample point f' = + or - Show inc/dec 2nd derivative information Interval Sample point f" x f" = + or - Concavity:
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:...
Determine the intervals on which f is increasing or decreasing, assuming the figure below is the graph of the derivative of f. On Interval 1: is ? < On Interval 2: f is? On Interval 3: fis ? 241 24.1 1 & -2411 If the figure below is the graph of the derivative f', answer the following: Where do the points of inflection of f occur? On which interval(s) is f concave down? 4,
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