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Question 8 (9 marks) For the function given by f(x) = are arctan(r3), find (a) dom(f)...
Determine the intervals on which the given function is concave up or down and find the...
Determine the intervals on which the given function is concave up or down and find the point of inflection. Let f(x) = x(x - 5) The x-coordinate of the point of inflection is 225/64 , and on this interval f is The interval on the left of the inflection point is Concave Down The interval on the right is Concave Up and on this interval f is Determine the intervals on which the given function is concave up or down...
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of...
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b)...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f....
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
Consider the following. f(x) = - *** + 3x3- 1/3 - 3x2 + 8 Find f'(x)....
Consider the following. f(x) = - *** + 3x3- 1/3 - 3x2 + 8 Find f'(x). f'(x) = Find F"(x). f"(x) = Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) X = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using interval notation.) Locate the points of inflection. (If an answer...
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.
2. for the function f(x)= x+2 cos x on the interval [0,2pi] a. find the first...
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...
Let f(x) = 2x + 8/x +1 (a) Find the interval(s) where the function is increasing...
Let f(x) = 2x + 8/x +1
(a) Find the interval(s) where the function is increasing and
the interval(s) where it is decreasing. If the answer cannot be
expressed as an interval, state DNE (short for does not exist).
(b) Find the relative maxima and relative minima, if any. If
none, state DNE.
(c) Determine where the graph of the function is concave upward
and where it is concave downward. If the answer cannot be expressed
as an interval, use...
7. [23] Given the following function:: f(x)-x-4x +6 (a) Find all of the critical points of...
7. [23] Given the following function:: f(x)-x-4x +6 (a) Find all of the critical points of this function. Show your work. (b) Characterize each of the critical points as a local maximum, a local minimum or neither. Show your work. (c) Find all of the inflection points of this function (verify that it/they are indeed inflection points). (d) On what interval(s) is this function both decreasing and concave down? on the interval -15xs1. Show (e)Find the global maximum and minimum...
Consider the function below. f(x) = x^2 / ( x - 8 ) ^2 (a) Find...
Consider the function below. f(x) = x^2 / ( x - 8 ) ^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter your answer using interval notation.) (c) Find the local minimum value. (d) Find the inflection point. (x, y) = e :Find the interval where the function is concave up. (Enter your answer using...
Determine the intervals on which the given function is concave up or down and find the point of inflection. Let f(x) = x(x - 5) The x-coordinate of the point of inflection is 225/64 , and on this interval f is The interval on the left of the inflection point is Concave Down The interval on the right is Concave Up and on this interval f is Determine the intervals on which the given function is concave up or down...
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
Consider the following. f(x) = - *** + 3x3- 1/3 - 3x2 + 8 Find f'(x). f'(x) = Find F"(x). f"(x) = Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) X = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using interval notation.) Locate the points of inflection. (If an answer...
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.
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...
Let f(x) = 2x + 8/x +1
(a) Find the interval(s) where the function is increasing and
the interval(s) where it is decreasing. If the answer cannot be
expressed as an interval, state DNE (short for does not exist).
(b) Find the relative maxima and relative minima, if any. If
none, state DNE.
(c) Determine where the graph of the function is concave upward
and where it is concave downward. If the answer cannot be expressed
as an interval, use...
7. [23] Given the following function:: f(x)-x-4x +6 (a) Find all of the critical points of this function. Show your work. (b) Characterize each of the critical points as a local maximum, a local minimum or neither. Show your work. (c) Find all of the inflection points of this function (verify that it/they are indeed inflection points). (d) On what interval(s) is this function both decreasing and concave down? on the interval -15xs1. Show (e)Find the global maximum and minimum...
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