Each of Exercises 81–84 shows the graphs of the first and seconderivatives of a function y = f(x). Copy the picture and add to itsketch of the approximate graph of f, given that the graph passethrough the point P.81.82.yy = f'(x)хPey = f"(x)y = f"(x),83. yPoy = f'(x)y = f"(x)84.y = f'(x)хy = f"(x)

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Answered: Each of Exercises 81–84 shows the…

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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The sales of a book publicationare expected to grow according to the function S = 300000(1 - e-0.06t), where t is the time, given in days. 1. Show using differentiation that the sales never attains an exact maximum value. 2. What is the limiting value approached by the sales function?
Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2 where x, y,and z are measured in meters, and you are standing at a point with coordinates (60, 40, 966). The positivex−axis points east and the positive y−axis points north.If you walk northwest from point P, will you start to ascend or descend? At what rate? To answer this, do I need to make my function f(x,y) and then take the gradient, or do I need it to be f(x,y,z) and then take the gradient?
Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. C(t) = (e−αt − e −βt )/(β − α) , where α and β are constants with β > α > 0. (a) Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) (b) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)
Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does the graph of ƒ have a local maxi-mum, local minimum, or point of inflection?
If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f (x) = 1 / y (x), what is the average rate of change of the function f ( x) In the same period ?!
Suppose that the only information we have about a function fis that f(1) = 5 and the graph of its derivative is as shown.(a) Use a linear approximation to estimate f(0.9) and f(1.1).(b) Are your estimates in part (a) too large or too small?Explain.
On the graph of f(x) = cotx and the interval [ − 2π, 0π ), for what value(s) of x does f(x) = 1?
find the first derivative and solve it for x after setting it to zero. Substitute the x-values obtained as well as your endpoints into the original functions to observe the y-values. Only subs x-values that lie within the closed interval given.
Explain in your own words, how do you find the followings using first and second derivatives of function f(x): a- minimum and maximum points for function f(x) b- increasing and decreasing intervals for f(x) c- concave up or concave down intervals for f(x) d- point of inflection for f(x)
find the value of the constant c that makes the attached function continuous on (-∞, ∞) c =
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