4. For the following function f find the domain; the asymptotes ;intervals where f is increasing, decreasing, concave upward, concave downward; local maximum, minimum and inflection points; sketch the graph: f(x) = 1/(x-1)3
For the following function f find the domain; the asymptotes ;intervals where f is increasing, decreasing, concave upward, concave downward
Find where the graph of f is increasing, decreasing, concave upward and concave downward then find any intercepts, relative extrema, points of inflection, and asymptote. Use this information to sketch the graph of f.f(x) = (2x-1)2(x-3) (x-7)
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.
$$ y=\frac{6\left(x^{2}-1\right)}{x^{2}+3} \quad \underline{\text { Note }}: y^{\prime}=\frac{48 x}{\left(x^{2}+3\right)^{2}}, \quad y^{\prime \prime}=\frac{144\left(1-x^{2}\right)}{\left(x^{2}+3\right)^{3}} $$Sketch the graph of each of the following, giving intercepts, asymptotes, where increasing. where decreasing, any relative maximum and relative minimum points, where concave upward, where concave downward, and any inflection points.
Sketch the graph of f(x)= (x^2)/(x^2-1), stating all relative extreme points, intervals of increasing and decreasing, intervals of concave up and concave down, inflection points, and asymptotes.
2) Determine the intervals where the graph of the function is concave upward or concave downward. Find all the possible points of inflection. (x) - X-sinx,Os X s 2
Find the largest open intervals on which the function is concave upward or concave downward, and find the location of any points of inflection. f(x) = -x - = -x - 3x +4 Select the correct choice below and fill in the answer box(es) to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) O A. The function is concave upward on...
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).
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...
1. (30 pts.) Given that. (.r) = Determine 22-1 (a) The domain and intercepts of f. (b) Asymptotes off. (c) The intervals where f is increasing and where f is decreasing, (d) Local minimum and maximum values off. (e) Intervals where f is concave up and where f is concave down, (S) Inflection point off, (9) Sketch the graph of f. (You have to show all steps clearly otherwise you won't be awarded any credit)
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...