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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...
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?
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. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I ...
7. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I spilled my tea on the graph of f(x). The coffee dissolved the ink as shown. Please redraw the graph for me using the graph of f(x). (Hint: Graph f"(x) to determine the concavity of the original graph.) Be sure to indicate important features like relative max and min, points of inflection, increasing and decreasing intervals, and intervals where the graph is concave up...
Given the function: f(x)=(x^2-4x+6)/(x-1)^2 a) Find the asymptotes of f, if any b) Find the first...
Given the function: f(x)=(x^2-4x+6)/(x-1)^2 a) Find the asymptotes of f, if any b) Find the first and the second derivatives of f c) Find the intervals of increase and decrease of f d) Find the relative maxima and the relative minima, if any e) Find the intervals where f is concave up and down, respectively, together with the points of inflection, if any.
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...
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 following function. (If an answer does not exist, enter UN 36 f(x) = x...
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 1 a f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1) d. f(2)= 2 e...
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...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 -...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 - 2 Moreover, f'(0) = 0 and f(1) = 0. (a) Find the function f(x). (b) Draw a graph of f(x). Indicate all asymptotes (if any), local maxima and minima, inflection points, intervals where f(x) is increasing, and intervals where f(x) is concave upward.
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?
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. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I spilled my tea on the graph of f(x). The coffee dissolved the ink as shown. Please redraw the graph for me using the graph of f(x). (Hint: Graph f"(x) to determine the concavity of the original graph.) Be sure to indicate important features like relative max and min, points of inflection, increasing and decreasing intervals, and intervals where the graph is concave up...
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...
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 following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
(20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function fis decreasing, increasing, concave up, and concave down List the x-coordinates of all local maxima and minima, and points of inflection. Show asymptotes with dashed lines and give their equations. Label all important points on the graph. 1 a f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1) d. f(2)= 2 e...
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...
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 - 2 Moreover, f'(0) = 0 and f(1) = 0. (a) Find the function f(x). (b) Draw a graph of f(x). Indicate all asymptotes (if any), local maxima and minima, inflection points, intervals where f(x) is increasing, and intervals where f(x) is concave upward.
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