. Consider the function f(x) = 2x^ 3 + 9x^ 2 − 24x + 1. (1)...
. Consider the function f(x) = 2x^ 3 + 9x^ 2 − 24x + 1. (1) (5 points) Find all the critical points of f(x).
(2) (5 points) Find the intervals on which f(x) is increasing and decreasing, and find the x-values of any relative minima/maxima.
Homework Answers
1. (1 point) Let f(x) = -3 - 9x? +152 +5. Find the open intervals on...
1. (1 point) Let f(x) = -3 - 9x? +152 +5. Find the open intervals on which is increasing (decreasing). Then determine the 2-coordinates of all relative maxima (minima). f is increasing on the intervals f is decreasing on the intervals 3. The relative maxima of foccur at 2 = 4. The relative minima off 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...
1. For f(x) = 924 – 2x a) Find the critical value(s). b) Find the open...
1. For f(x) = 924 – 2x a) Find the critical value(s). b) Find the open intervals over which the function is increasing or decreasing, c) Find the point(s) of any relative maxima or relative minima.
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
Answer the following questions about the function whose derivative is f'(x) = 2x(x - 5), a....
Answer the following questions about the function whose derivative is f'(x) = 2x(x - 5), a. What are the critical points of f? b. On what open intervals is fincreasing or decreasing? c. At what points, if any, does fassume local maximum and minimum values? a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The critical point(s) of fis/are x = (Simplify your...
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...
(1 point) Let f(x) = 6x + Find the open intervals on which f is increasing...
(1 point) Let f(x) = 6x + Find the open intervals on which f is increasing (decreasing). Then determine the e-coordinates of all relative maxima (minima) 1. f is increasing on the intervals (-INF-sqrt(1/3)U(sqrt(1/3).INF) 2. fis decreasing on the intervals (-sqrt(1/3).0)0(0,sqrt(1/3)) 3. The relative maxima off occur at sqrt(1/3) 4. The relative minima off occur at z = sqrt(1/3) Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of...
Consider the function on the interval (0, 2). f(x) = sin(x) cos(x) + 8 (a) Find...
Consider the function on the interval (0, 2). f(x) = sin(x) cos(x) + 8 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (larger x-value) (X,Y)= (x, y) = (1 (x, y) = relative minima (smaller x-value) (larger x-value)
need help with these.please. I-8 Let f(2) Find the open intervals on which fis increasing (decreasing)....
need help with these.please.
I-8 Let f(2) Find the open intervals on which fis increasing (decreasing). Then determine the x-coordinates of +8 all relative maxima (minima). 1. f is increasing on the intervals 2. fis decreasing on the intervals 3. The relative maxima of f occur at - 4. The relative minima off 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...
For the function below, determine each of the following. g(x) = x^4 / (x − 24)...
For the function below, determine each of the following. g(x) = x^4 / (x − 24) (a) Find the critical values of g(x). (Enter your answers as a comma-separated list.) (b) Find the intervals on which g(x) is increasing and the intervals on which g(x) is decreasing. Enter your answers using interval notation. Increasing: Decreasing: (c) Find the x-coordinates of all relative extrema on the graph of g(x). (Enter your answers as a comma-separated list. If an answer does not...
1. Consider the function f(x) = xe-* a) On what interval, if any, is the function...
1. Consider the function f(x) = xe-* a) On what interval, if any, is the function f(x) increasing? b) For what value(s) of x does the function have any relative maxima or minima? c) On what intervals, if any, is the graph of f(x) concave down? d) For what value(s) of x, if any, does the the function have a point of inflection?
1. (1 point) Let f(x) = -3 - 9x? +152 +5. Find the open intervals on which is increasing (decreasing). Then determine the 2-coordinates of all relative maxima (minima). f is increasing on the intervals f is decreasing on the intervals 3. The relative maxima of foccur at 2 = 4. The relative minima off 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...
1. For f(x) = 924 – 2x a) Find the critical value(s). b) Find the open intervals over which the function is increasing or decreasing, c) Find the point(s) of any relative maxima or relative minima.
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
Answer the following questions about the function whose derivative is f'(x) = 2x(x - 5), a. What are the critical points of f? b. On what open intervals is fincreasing or decreasing? c. At what points, if any, does fassume local maximum and minimum values? a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The critical point(s) of fis/are x = (Simplify your...
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...
(1 point) Let f(x) = 6x + Find the open intervals on which f is increasing (decreasing). Then determine the e-coordinates of all relative maxima (minima) 1. f is increasing on the intervals (-INF-sqrt(1/3)U(sqrt(1/3).INF) 2. fis decreasing on the intervals (-sqrt(1/3).0)0(0,sqrt(1/3)) 3. The relative maxima off occur at sqrt(1/3) 4. The relative minima off occur at z = sqrt(1/3) Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of...
Consider the function on the interval (0, 2). f(x) = sin(x) cos(x) + 8 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (larger x-value) (X,Y)= (x, y) = (1 (x, y) = relative minima (smaller x-value) (larger x-value)
need help with these.please.
I-8 Let f(2) Find the open intervals on which fis increasing (decreasing). Then determine the x-coordinates of +8 all relative maxima (minima). 1. f is increasing on the intervals 2. fis decreasing on the intervals 3. The relative maxima of f occur at - 4. The relative minima off 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...
1. Consider the function f(x) = xe-* a) On what interval, if any, is the function f(x) increasing? b) For what value(s) of x does the function have any relative maxima or minima? c) On what intervals, if any, is the graph of f(x) concave down? d) For what value(s) of x, if any, does the the function have a point of inflection?
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