True or false: 7. The points of inflection are found by solving the first derivative equal to Zero 8. When the denominator of a rational function is zero the function will always have a vertical asymptote 9. To determine the behavior of a function near the vertical asymptotes we use left and right-hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test 11.A function can never cross asymptotes 12.To determine the end behavior of

True or false: 7. The points of inflection are found by solving the first derivative equal to Zero 8. When the denominator of a rational function is zero the function will always have a vertical asymptote 9. To determine the behavior of a function near the vertical asymptotes we use left and right-hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test 11.A function can never cross asymptotes 12.To determine the end behavior of

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
1. Determine the slope of the tangent line to the function f(x) = 2 x+1at x = 5. 2. Explain the graphical and algebraic differences between average rate of change and instantaneous rate ofchange. 3. Explain the two types of discontinuities that may exist in a rational function, and how to distinguishbetween the two types algebraically and graphically.
The sales of a book publication are expected to grow according to the function S=300000(1-e^-0.06t) where g is the time , given in days showing using differentiation that the sales never attains an exact maximum value. What is the limiting value approach by the sales function? A poll commissioned by a politician estimates that t after he makes a statement, denegrating women, the percentage of his constituency( those who support him at the time he made the statement) that still supports him is given by S(t)=75(t^2-3t+25)/t^2+3t+25 The election is 10 days after he made the statement if derivatives S'(t) may be thought of as an approval rate, derivate the function for his approval rate. When was his support at its lowest? What was his minimum support level? Was the approvals rate positive or negative on the date of the election
Please, I need the answers of other tutors to check, thank you very much!Find the vertical and horizontal asymptotes of f(x), find the first and second derivatives and draw the graph of the following function. Be precise on the values in the range -4 to 4 and on the critical values of the derivatives: f(x)= ( (x^3)+8) / ((x^3-8)) How would the graph change if it were f(x) = ( (x^3)+8) / ((x^3-8)) +1
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?
a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?
We have determined that there are two points where the slope of the tangent line is equal to 0. One where x = −6 and one where x = 6. Note that the rational functions f(x) and f '(x) are defined at these values. To find the y-value of the point where x = −6, substitute −6 for x in the function f(x)= x/x2+36 f(-6)= -6/(-6)2+36 Therefore, one of the points where the slope of the tangent line is horizontal is (x, y) =
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
1) Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2, but I am confused on how to get f"(x). 2) If a rock is thrown upward on Mars with a velocity of 15 m/s, its height in meters after t seconds is given by h=15t - 1.86t2. I need help starting this problem 3) lim (x--> inf) arctan(x2-x7) I need help starting the problem
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.)
Shown is the graph of the derivative f'(x) of the function f(x). (a) Identify the critical numbers of f(x). (b) For each critical value, determine whether it is a local maximum, local minimum, or neither. (c) Is f''(−2) positive or negative? What can you say about the concavity of the original function f(x) nearby x = −2?
On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?