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5. (13 pts) (x) = 2x° -6x° -18x a. Find the location of the local maximum(s)...
1-Find the local maximum value of f using both the First and Second Derivative Tests. f(x)...
1-Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + √4 - x 2-Consider the equation below. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.) f(x) = 2x3 + 3x2 − 72x (a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.) ( , ) ∪ ( , ) Find the interval on which f is decreasing. ( , ) (b) Find the local minimum and...
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which...
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which f(x) is increasing and decreasing. 6 Find any local maximum and minimum c) Find intervals over which the graph off is concave upward, and concave downward. Id Find any inflection points. e) Use the above results to graph FX).
5. (4pts, each) In each part, list the point (A-E) on the graph off whose x-coordinate...
5. (4pts, each) In each part, list the point (A-E) on the graph off whose x-coordinate satisfies the given conditions. (a) f'(x) > 0. and F"(x) > 0 (b) f'(x) <0. and f"(x) = 0 (c) f'(x) = 0.and f"(x) < 0 6. (12pts) Find all critical numbers of f(x) = x + Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Show your work to get a full...
Use the first derivative test to determine the location of each local extremum and the value...
Use the first derivative test to determine the location of each local extremum and the value of the function at this extremum. - 2x f(x) = x 6 Identify the location and function value of the maximum of the function, if any. Select the correct answer below and, if necessary, fill in any answer boxes within your choice. O A. The function has a local maximum of at x = (Use a comma to separate answers as needed. Type exact...
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)...
show work 2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f...
show work
2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
Consider the function f(x) = 2x + 6x2 - 144x + 6. For the following questions,...
Consider the function f(x) = 2x + 6x2 - 144x + 6. For the following questions, write inf for 0, -inf for --O, U for the union symbol, and NA (ie. not applicable) if no such answer exists. a.) f'(x) = 6x^2+12X-144 b.) f(x) is increasing on the interval(s) c.) f(x) is decreasing on the interval(s) d.)f(x) has a local minimum at NA e.)f(x) has a local maximum at NA f.)f"(x) = 12x+12 g.)f(x) is concave up on the interval(s)...
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. f(x) = x? – 3x² +5. a) (5 pts) Find the (x, y) coordinates of...
2. f(x) = x? – 3x² +5. a) (5 pts) Find the (x, y) coordinates of the critical points. b) (5 pts) Find the (x, y) coordinates of the point of inflection (point of diminishing return) c) (5 pts) Over what interval is the function increasing/decreasing and over what interval is the function concave up/concave down? Analytically test for concavity. d) (5 pts) Use the 2nd derivative test to determine (x, y) coordinates of the relative max/min.
17. Given the following function and its first and second derivative: 20-2 6-43 f'(x)= f"(x) =...
17. Given the following function and its first and second derivative: 20-2 6-43 f'(x)= f"(x) = [2 pts] 1) Find the horizontal and vertical asymptotes of f(x), if any. f(x)=x-2x=1 نر [2 pts) ii) Find all critical numbers. Note: NOT a point, just critical numbers only. [5 pts) iii) Find the intervals of increasing and decreasing then finding all local maximum minimum values. [5 pts] Find the intervals of concave upward and concave downward. [2 pts) Find inflection point, if...
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which f(x) is increasing and decreasing. 6 Find any local maximum and minimum c) Find intervals over which the graph off is concave upward, and concave downward. Id Find any inflection points. e) Use the above results to graph FX).
5. (4pts, each) In each part, list the point (A-E) on the graph off whose x-coordinate satisfies the given conditions. (a) f'(x) > 0. and F"(x) > 0 (b) f'(x) <0. and f"(x) = 0 (c) f'(x) = 0.and f"(x) < 0 6. (12pts) Find all critical numbers of f(x) = x + Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Show your work to get a full...
Use the first derivative test to determine the location of each local extremum and the value of the function at this extremum. - 2x f(x) = x 6 Identify the location and function value of the maximum of the function, if any. Select the correct answer below and, if necessary, fill in any answer boxes within your choice. O A. The function has a local maximum of at x = (Use a comma to separate answers as needed. Type exact...
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)...
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2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
Consider the function f(x) = 2x + 6x2 - 144x + 6. For the following questions, write inf for 0, -inf for --O, U for the union symbol, and NA (ie. not applicable) if no such answer exists. a.) f'(x) = 6x^2+12X-144 b.) f(x) is increasing on the interval(s) c.) f(x) is decreasing on the interval(s) d.)f(x) has a local minimum at NA e.)f(x) has a local maximum at NA f.)f"(x) = 12x+12 g.)f(x) is concave up on the interval(s)...
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. f(x) = x? – 3x² +5. a) (5 pts) Find the (x, y) coordinates of the critical points. b) (5 pts) Find the (x, y) coordinates of the point of inflection (point of diminishing return) c) (5 pts) Over what interval is the function increasing/decreasing and over what interval is the function concave up/concave down? Analytically test for concavity. d) (5 pts) Use the 2nd derivative test to determine (x, y) coordinates of the relative max/min.
17. Given the following function and its first and second derivative: 20-2 6-43 f'(x)= f"(x) = [2 pts] 1) Find the horizontal and vertical asymptotes of f(x), if any. f(x)=x-2x=1 نر [2 pts) ii) Find all critical numbers. Note: NOT a point, just critical numbers only. [5 pts) iii) Find the intervals of increasing and decreasing then finding all local maximum minimum values. [5 pts] Find the intervals of concave upward and concave downward. [2 pts) Find inflection point, if...
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