Chapter 4 tch the graph. Each part Use the function below on the interval specified to answer the...
2. for the function f(x)= x+2 cos x on the interval [0,2pi] a. find the first derivative b.) find the second derivative c.) find the functions critical values(if any). include their y- coordinates in your answers in order to form critical points. d. )find the intervals on which f is increasing or decreasing. e. )find the local extrema of f. f. )find the functions hyper critical values(if any). include their y coordinates g.) find the intervals of concavity, i.e. the...
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
1. Consider the curve given by the function f(x) = -4.83 27(x + 1)2 You are given that -4x²(x +3) - 8.1 f'(x) = and f"(x) = 27(x + 1)3 9(x + 1)4 Compile the following information about f(x) and its graph. Show your work to justify your answers to parts (f), (g), (h), (i) and (j). Otherwise, give answers only. Answer "NONE” if the function does not display a feature listed. 1] (a) Domain of f (b) x and...
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...
(1 point) NOTE: When using interval notation in WebWork, remember that: You use 'INF' for oo and '-INF' for -0. And use 'U' for the union symbol. Enter DNE if an answer does not exist. f(x) = -1.5x² – 5x – 2 a) Determine the intervals on which f is concave up and concave down. f is concave up on: f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each...
Each letter is a different part of the same question. Therefore, please fill in all of the individual blanks. Thanks in advance Suppose that f(x) = x4 + 12x3. (A) Use interval notation to indicate where f(x) is defined. If it is defined on more than one interval, enter the union of all intervals where f(x) is defined. Domain: (B) Find all intercepts. If there are no intercepts, enter None. If there are more than one, enter them separated by...
2. Consider the function f(x) = sinx 2+cos a) What is the domain of the function? b) Use the first derivative to locate the intervals of increase or decrease as w e the intervals of increase or decrease as well as any local your analysis to the intervalo Sxs 21. Indicate the exact coordinates of the al extrema and clearly specify whether the point is a local max or local min. use the second derivative to determine intervals of concavity...
question 9 from A to F 9. (5 points) Please answer the following questions about the function fr) - 21² f(x) = 2.9 al num- increas- for the Instructions: . If you are asked for a function, enter a function. - If you are asked to find X- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. . If you are asked to find an interval or union...
(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...