Cells in tissue attach to each other through membrane bound adhesion molecules. Many cells extend protrusions or fillipodia to make adhesion bonds further away than one cell radius. We assume that the cell adhesion force f (x) of a given cell depends on the distance x to the neighboring cell, and is given by 4x f(x) = 1+ x² ° (a) Find the vertical and horizontal asymptotes of f (x). (b) Find local maxima and minima and intervals of increase and decrease of f(x). (c) Find inflection points and intervals of concavity of f (x).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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Section5.2: Power Functions
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Problem 1: Cell Adhesion
Cells in tissue attach to each other through membrane bound adhesion molecules. Many cells extend protrusions or fillipodia to make adhesion bonds further
away than one cell radius. We assume that the cell adhesion force f (x) of a given cell depends on the distance x to the neighboring cell, and is given by
4x
f(x) =
1 + x² °
(a) Find the vertical and horizontal asymptotes of f(x).
(b) Find local maxima and minima and intervals of increase and decrease of f (x).
(c) Find inflection points and intervals of concavity of f (x).
(d) Sketch the graph of f (x).
(e) Explain the shape of f(x) in biological terms.
Transcribed Image Text:Preview Problem 1: Cell Adhesion Cells in tissue attach to each other through membrane bound adhesion molecules. Many cells extend protrusions or fillipodia to make adhesion bonds further away than one cell radius. We assume that the cell adhesion force f (x) of a given cell depends on the distance x to the neighboring cell, and is given by 4x f(x) = 1 + x² ° (a) Find the vertical and horizontal asymptotes of f(x). (b) Find local maxima and minima and intervals of increase and decrease of f (x). (c) Find inflection points and intervals of concavity of f (x). (d) Sketch the graph of f (x). (e) Explain the shape of f(x) in biological terms.
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