Answered: The function f graphed below is defined…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.3: Getting Information From The Graph Of A Function

Problem 4E: The function f graphed below is defines by a polynomial expression of degree 4. Use the graph to...

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The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise.
yA
(a) A function value f(a) is a local maximum value of f if f(a) is the ---Select--- v value of f on some open interval containing a. From the graph of f we see that there are two local maximum values of f: one local maximum is
and it occurs when x = 2; the other local maximum is
and it occurs when x =
(b) The function value f(a) is a local minimum value of f if f(a) is the ---Select-- v value of f on some open interval containing a. From the graph of f we see that there is one local minimum value of f. The local minimum
value is
and it occurs when x =

Expert Solution

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From the given graph, we observed that the function $f$ has two points, which are local maxima, and one point where f attains local minima. $f$ attains local maximum at $x = 2, f (2) = 7$ and $x = 5, f (5) = 6$ . $f$ attains local minimum at $x = 4, f (4) = 2$ . Therefore,

(a)

A function value $f (a)$ is a local maximum value of $f$ is the Largest value of $f$ on some open interval containing $a$ . From the graph of $f$ we see that there are two local maximum values of $f$ , one local maximum is $7$ , and it occurs when $x = 2$ ; the other local maximum is $6$ , and it occurs when $x = 5$ .

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