find A B and C Consider the function f(x) = 3x + 8x-¹. For this function there are four important intervals:1(-∞o, A], [A, B), (B, C], and [C, ∞o) where A, and C are the critical numbers and the function is notdefined at B.Find Aand Band CFor each of the following open intervals, tell whether f(x) is increasing or decreasing.(-∞, A): Increasingor(A, B): Decreasing(B, C): Decreasing(C, ∞) Increasing>OFooorNote that this function has no inflection points, but we can still consider its concavity. For each of thefollowing intervals, tell whether f(x) is concave up or concave down.(-∞o, B): Concave Down(B, ∞): Concave UpQuestion Help: VideoorOuSubmit Question Jump to Answer

Use differentiation for finding A and B and C

Consider the function f(x) = 3x + 8x-1. For this function there are four important intervals: (-∞o, A], [A, B), (B, C], and [C, oo) where A, and C are the critical numbers and the function is not defined at B. Find A and B and C For each of the following open intervals, tell whether f(x) is increasing or decreasing. (-∞o, A): Increasing (A, B): Decreasing (B, C): Decreasing (C, ∞) Increasing Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) is concave up or concave down. (-∞o, B): Concave Down (B, ∞o): Concave Up Question Help: Video OT

Consider the function f(x) = 3x + 8x-1. For this function there are four important intervals: (-∞o, A], [A, B), (B, C], and [C, oo) where A, and C are the critical numbers and the function is not defined at B. Find A and B and C For each of the following open intervals, tell whether f(x) is increasing or decreasing. (-∞o, A): Increasing (A, B): Decreasing (B, C): Decreasing (C, ∞) Increasing Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) is concave up or concave down. (-∞o, B): Concave Down (B, ∞o): Concave Up Question Help: Video OT

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 11T: Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6...

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Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.
Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.