1. Determine the following information regarding each function step by step and then sketchits graph off(x)=7x²_7f(x )f '(x )f"(x )• Intervals of increaseand decreaseCoordinates of anylocal/absoluteIntervals of concavityCoordinates of anypoints of inflectionDomainx and y interceptsVerticalasymptote(s) andbehaviour of f(x) atvertical asymptote(s)(one-sided limits)• Horizontal/Obliqueasymptote and endbehaviour of f(x)(limits to infinity)maximum andminimum points

Answered: 1. Determine the following information…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f.
2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x^2)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f. b. Find the intervals on which the graph of f is increasing or decreasing.
(i) Discuss the continuity of the function f(x) = {x2 − 3x if x < 2 2x + 4 if x ≥ 2ontheopeninterval0< x<2andontheclosedinterval0≤x≤2.(ii) Anefficiencystudyofthemorningshiftatacertainfactoryindicatesthatanaverage worker arriving on the job at 7: 00 A. M. will have assembled f (x) = x3 + 6x2 + 15x units x hours later. Approximately how many units will the worker assemble between8:00and8:15A.M.?(iii) A manufacturer’s total cost is C(q) = 0.1q3 + 0.5q2 + 500q + 200dollars when the level of production is q units.The current level of production is 4 units, and the manufacturer is planning to increase this to 4.1 units. Estimate how the total cost will change as a result.
If the above graph is the graph of f′(x), then f(x) has a local maximum at x=___, a local minimum at x=____ and a critical point that is neither a local maximum nor a local minimum at x=____
1)if the line x=0 is a vertical asymptote of y=f(x) then the function is not defined at x=0 true or false.
Use a graph below of f(x) = ln (3x^2 +1) to estimate the x-values of any critical points and inflection points of f(x).
1.) The cost, in thousands of dollars, of airing x 30-second television commercials during a major football game can be approximated by C(x) = 20 + 4000x + 0.05x^2 How many 30-second television commercials should your company air to minimize average costs? What is the resulting average cost of a 30-second ad? 2.) Find the exact location of all the relative and absolute extrema of the function: f(x) = 5x^3 − 60x with domain [−4, 4]
Generate a continous and differentiable functiin f(x) with the following properties: f(x) is decreasing at x=-6, f(x) has a local minimum at x= -3, f(x) has a maximum at x= 3
Your are asked to generate a continuous and differentiable function f(x) with the following properties. f(x) is decreasing by x=-5 f(x) has a local minimum at x= -2 f(x) has a local maximum at x= 2
The question is about bounded variation. When I trying to use the hint to fix this problem, I have no idea that how can I try to find F(x)=g(x)-h(x) and let g(x) and h(x) are monumentally increasing function
Suppose that f ‘(x) is negative for x < 1 and positive for x > 1. Does f have a local minimum or maximum value at x = 1?
The function y = 1/x does not take on either a maximum or a minimum on the interval 0 < x < 1 even though the function is continuous on this interval. Does this contradict the Extreme Value Theorem for continuous functions? Why?

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