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)
Find where the graph of f is increasing, decreasing, concave upward and concave downward
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
$$ y=\frac{6\left(x^{2}-1\right)}{x^{2}+3} \quad \underline{\text { Note }}: y^{\prime}=\frac{48 x}{\left(x^{2}+3\right)^{2}}, \quad y^{\prime \prime}=\frac{144\left(1-x^{2}\right)}{\left(x^{2}+3\right)^{3}} $$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.
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...
determine where the graph of the function f(x)=2x-√49-x^2 is concave upward and where it is concave downward. also find all inflection points of the function (In 73.1 In 8 7211 Оe 1 94 721 dla 1 QUESTION 4 Determine where the graph of the function f(x)-2x-19-x is concave upward and where it is concave downward. Also find all infection points of the function O a CD on (-7, 7). IP mone b. CU en (-7,7 IP none OC CU on...
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. X +3 f(x) = x²-x-12 On what interval(s) is fincreasing and on what interval(s) is f decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The...
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down, locate inflection pts. Use this information to sketch the graph. (20 pts) 4x2 + 12x – f'(x) = Critical Values are: F"(x) = Possible Inflection points are: First derivative information Interval Sample point f' = + or - Show inc/dec 2nd derivative information Interval Sample point f" x f" = + or - Concavity:
Let. Fox , FO) = * F"(x) = 2XT9 1.Find x-and y-intercepts of the graph of f, if it has any. 2. Find vertical and horizontal asymptote(s) of f, if it has any. 3. Find the critical number(s), intervals(s) of increasing and decreasing and points of relative extrema off, if it has any. 4. Find intervals of concavity and the point(s) of inflection of f, if any Page 2 5. Sketch the graph of f, label all important points from...
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...
2. Determine where the functions below are increasing and decreasing, and where in the graphs they are concave up and concave down. Find the relative extrema and inflection points. a. g(x)=V?+1 b. f(x)=
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