Stedent D Name 9.20 pts) ldentify the following information and sketch the graph of fix)-x+4x (a)a...
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.
12. (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. a. f(x) is defined for all real numbers 2x b. f(x) = -1 2 c. f'(x) - d. f(2)...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is 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 2 a. f(x) is defined for all real numbers 2x b. f'(x) = c. f"(x) = (x-1)...
12. (20 points) Sketch the graph of the function f(x) which satisfies the following conditions. Using interval notation list all intervals where the function f is 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. 2x X-1 2. a. f(x) is defined for all real numbers b. f'(x) = c. f"(x) = (x-1)2...
(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...
2. Use the information in the charts to answer the following questions and sketch the graph of the function f(x) a) List all the critical points (both coordinates) and classify them as max, min, or neither b) List all the inflection points - ND + + ND - 0 + S. Sketch the graph of each given function by doing the following (box your answer to each of the questions) 1. Determine the domain of the function. Use limits to...
> Derivatives and the shape of a graph 4- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down, and d. the inflection points off 226. f(x)= x4 - 6x3 228. f(x)= x + x2-r3 5- For the following exercises, determine a. intervals where fis increasing or decreasing, b. local minima and maxima off, c. intervals where fis concave up and concave down,...
(1 point) Suppose that f(x) = (??-9) (A) Find all critical values off. If there are no critical values, enter - 1000. If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f(x) is increasing. Note: When using interval notation in WeWork, you use I for 00,- for -00, and for the union symbol. If there are no values that satisfy the required condition, then enter ")" without the...
(A) Find all critical values off. If there are no critical values, enter None. If there are more than one enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f(a) is increasing. If it is increasing on more than one interval, enter the union of all intervals where f(a) is increasing Increasing: (C) Use interval notation to indicate where f(a) is decreasing. If it is decreasing on more than one interval, enter the union...
5. Letf(x) = x3 + x2 - x - 1. a. 6 pts Find all critical values off. Show all work. Answers from a graph will not receive full credit. b. 6 pts Make a sign chart for f'(x). c. 4 pts List the x and y coordinates of all local maxima and minima on the graph off. Clearly identify if the point is a maximum or minimum. d. 6 pts Make a sign chart for f'(x). e. 4 pts...