Suppose f(x) = x + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in the interval [-4,-1]. (a) First, we show that f has a root in the interval (-4,-1). Since f is a choose function on the interval [-4,-1] and f(-4) and f(-1) = the graph of y = f(x) must cross the x-axis at some point in the interval (-4,-1) by the choose ◆. Thus, f has at least one root in the interval [-4, -1]. = (b) Second, we show that f cannot have more than one root in the interval [—4, -1] by a thought experiment. Suppose that there were two roots x = a and x = b in the interval [-4, -1] with a

Suppose f(x) = x + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in the interval [-4,-1]. (a) First, we show that f has a root in the interval (-4,-1). Since f is a choose function on the interval [-4,-1] and f(-4) and f(-1) = the graph of y = f(x) must cross the x-axis at some point in the interval (-4,-1) by the choose ◆. Thus, f has at least one root in the interval [-4, -1]. = (b) Second, we show that f cannot have more than one root in the interval [—4, -1] by a thought experiment. Suppose that there were two roots x = a and x = b in the interval [-4, -1] with a

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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