Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does not have two real roots. Proof: Suppose f(x) has two real roots a and b such that f(a) = f(b) = = Since the conditions of Rolle's theorem hold true for f on [a, b], there exists at least one number c in the interval (a, b) such that f'(c) = However, the derivative f'(x) = therefore, it is ? ✓for f'(x) = is always ? This contradicts the conclusion of Rolle's Theorem and, therefore, f ? have two real roots. and,

Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does not have two real roots. Proof: Suppose f(x) has two real roots a and b such that f(a) = f(b) = = Since the conditions of Rolle's theorem hold true for f on [a, b], there exists at least one number c in the interval (a, b) such that f'(c) = However, the derivative f'(x) = therefore, it is ? ✓for f'(x) = is always ? This contradicts the conclusion of Rolle's Theorem and, therefore, f ? have two real roots. and,

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 48E

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