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ESTION 6 (8 marks) Consider the function f(x) = 2 2+1 .) Find the interval(s) in...
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...
2. Consider the function f(x) = ln (x+4) [6-6+8-16 marks] Note: f'()1")*** 3(4-2) a) On which...
2. Consider the function f(x) = ln (x+4) [6-6+8-16 marks] Note: f'()1")*** 3(4-2) a) On which intervals is f(x) increasing or decreasing b) On which intervals is f(x) concave up or down? c) Sketch the graph of f(x) below Label any intercepts, asymptotes, relative minima, relative maxima and infection points
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...
6. Consider the function f(x) = x3 - 10x (a) (3 pts) Find f '(x) (b)...
6. Consider the function f(x) = x3 - 10x (a) (3 pts) Find f '(x) (b) (9 pts.) Find the intervals where f(x) is increasing/decreasing, and classify any local max/min. (c) (3 pts) Find f '(x) (d) (9 pts.) Find the intervals where f(x) is concave up/down and classify any inflection points. Using the information from parts a-d only, sketch the graph of y=f(x).
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval...
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
2. (4+6+2+4+2+6=24 points Consider the function f(x) = -1 (a) Find any vertical and horizontal asymptotes...
2. (4+6+2+4+2+6=24 points Consider the function f(x) = -1 (a) Find any vertical and horizontal asymptotes off. (b) On what intervals is f increasing? decreasing? (c) Find all local maximum and minimum values of (d) On what intervals is f concave up? concave down? (e) Find all inflection points of f. (f) Using the information from (a) to (e), sketch a graph of J. Clearly label any asymptotes, local extrema, and inflection points.
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...
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...
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)
3. On the open interval (0, π/2), a function f with f'(x) = sin(x^2 ) must...
3. On the open interval (0, π/2), a function f with f'(x) = sin(x^2 ) must be (choose one, and explain your answer): (a) increasing and concave up (b) decreasing and concave up (c) increasing and concave down (d) decreasing and concave up (e) None of the above
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...
2. Consider the function f(x) = ln (x+4) [6-6+8-16 marks] Note: f'()1")*** 3(4-2) a) On which intervals is f(x) increasing or decreasing b) On which intervals is f(x) concave up or down? c) Sketch the graph of f(x) below Label any intercepts, asymptotes, relative minima, relative maxima and infection points
6. Consider the function f(x) = x3 - 10x (a) (3 pts) Find f '(x) (b) (9 pts.) Find the intervals where f(x) is increasing/decreasing, and classify any local max/min. (c) (3 pts) Find f '(x) (d) (9 pts.) Find the intervals where f(x) is concave up/down and classify any inflection points. Using the information from parts a-d only, sketch the graph of y=f(x).
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
2. (4+6+2+4+2+6=24 points Consider the function f(x) = -1 (a) Find any vertical and horizontal asymptotes off. (b) On what intervals is f increasing? decreasing? (c) Find all local maximum and minimum values of (d) On what intervals is f concave up? concave down? (e) Find all inflection points of f. (f) Using the information from (a) to (e), sketch a graph of J. Clearly label any asymptotes, local extrema, and inflection points.
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...
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...
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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