A graph of y = f(x) is shown, where f(x) = 2x5 3x4 + x3 8x2 + 5x + 3 and f(x) = 2x5 3x4

Chapter 3, Problem 116

(choose chapter or problem)

A graph of y = f(x) is shown, where

\(f(x) = 2x^5 - 3x^4 + x^3 - 8x^2 + 5x + 3\) and \(f(-x) = -2x^5 - 3x^4 - x^3 - 8x^2 - 5x + 3\).

(a) How many negative real zeros does f have? Explain.

(b) How many positive real zeros are possible for f ? Explain. What does this tell you about the eventual right-hand behavior of the graph?

(c) Is \(x = -\frac{1}{3}\) a possible rational zero of f ? Explain.

(d) Explain how to check whether \((x -\frac{3}{2})\) is a factor of f and whether \(x = \frac{3}{2}\) is an upper bound for the real zeros of f.

Text Transcription:

f(x)=2x^5-3x^4+x^3-8x^2+5x+3

f(-x)=-2x^5-3x^4-x^3-8x^2-5x+3

x=-frac{1}{3}

(x-frac{3}{2})

x=frac{3}{2}