Homework Answers
Let f(x)=3x-7/x+2. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all infl...
Let f(x)=3x-7/x+2. Find the open intervals on which f is concave
up (down). Then determine the x-coordinates of all inflection
points of f.
Let Find the open intervals on which is concave up down Then determine the X-coordinates of all inflection points of x = f is concave up on the intervals 1. 2. f is concave down on the intervals 3· The inflection points occur at Notes: In the first two, your answer should either be a single interval,...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
Q-5: [5x1 marks] Let f(x) = 10 + (x – 2)4 a) Find f'(x) and f'(x)....
Q-5: [5x1 marks] Let f(x) = 10 + (x – 2)4 a) Find f'(x) and f'(x). b) Find the intervals on which f is increasing or decreasing. c) Find the local maximum and minimum of f, if any. d) Find the intervals on which the graph of f is concave up or concave down. e) Find the points of inflection, if any.
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are...
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are 1 + x2 2(1 – x2) 4x(x2 - 3) f'(x) = and f" (2) Using this information, (1 + x2) (1 + x2)3 (a) Find all relative extrema. (4 points) Minimum: Maximum: (b) Find the intervals of concavity for f(x) and identify any inflection points for yourself. (5 points) Concave up: Concave down: (c) Using the fact that lim f(x) = 1, and our...
conisder the following function: a)Find the x-intervals on which the graph of f is concave up,...
conisder the following function:
a)Find the x-intervals on which the graph of f is concave up,
and where it is concave down
b)Identify any inflection points on the graph of F.
f(x) = 23 – 9x2 - 4
5.1 - 2 (2 points) Let f(x) Find the open intervals on which f is concave...
5.1 - 2 (2 points) Let f(x) Find the open intervals on which f is concave up (down). Then determine the e-coordinates of all inflection points of 2 + 7 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at 2 - Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-int, 2),...
12. Determine the intervals on which the function f(x) = 3x5 - 10x3 + 12x -...
12. Determine the intervals on which the function f(x) = 3x5 - 10x3 + 12x - 5 is concave up or concave down and identify any inflection points. Write intervals in interval notation.
5 For the functions f(x) = (2,2 – 2x)e- and g(x) = 2.5 – 3.23 +...
5 For the functions f(x) = (2,2 – 2x)e- and g(x) = 2.5 – 3.23 + 22:2 (1) dentify and classify any stationary points using the second derivative test. (1) Identify and classify any points of inflection using the sign diagram of the second deriva- tive, (i) Determine the intervals where the function is concave up and concave down.
. Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x −...
. Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47 is concave down and up, along with the x-coordinates of any inflection points. Justify all your work
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...
Let f(x)=3x-7/x+2. Find the open intervals on which f is concave
up (down). Then determine the x-coordinates of all inflection
points of f.
Let Find the open intervals on which is concave up down Then determine the X-coordinates of all inflection points of x = f is concave up on the intervals 1. 2. f is concave down on the intervals 3· The inflection points occur at Notes: In the first two, your answer should either be a single interval,...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
Q-5: [5x1 marks] Let f(x) = 10 + (x – 2)4 a) Find f'(x) and f'(x). b) Find the intervals on which f is increasing or decreasing. c) Find the local maximum and minimum of f, if any. d) Find the intervals on which the graph of f is concave up or concave down. e) Find the points of inflection, if any.
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are 1 + x2 2(1 – x2) 4x(x2 - 3) f'(x) = and f" (2) Using this information, (1 + x2) (1 + x2)3 (a) Find all relative extrema. (4 points) Minimum: Maximum: (b) Find the intervals of concavity for f(x) and identify any inflection points for yourself. (5 points) Concave up: Concave down: (c) Using the fact that lim f(x) = 1, and our...
conisder the following function:
a)Find the x-intervals on which the graph of f is concave up,
and where it is concave down
b)Identify any inflection points on the graph of F.
f(x) = 23 – 9x2 - 4
5.1 - 2 (2 points) Let f(x) Find the open intervals on which f is concave up (down). Then determine the e-coordinates of all inflection points of 2 + 7 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at 2 - Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-int, 2),...
12. Determine the intervals on which the function f(x) = 3x5 - 10x3 + 12x - 5 is concave up or concave down and identify any inflection points. Write intervals in interval notation.
5 For the functions f(x) = (2,2 – 2x)e- and g(x) = 2.5 – 3.23 + 22:2 (1) dentify and classify any stationary points using the second derivative test. (1) Identify and classify any points of inflection using the sign diagram of the second deriva- tive, (i) Determine the intervals where the function is concave up and concave down.
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...
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