Consider the polynomial function f(x)= x^7 7 - x^6 6 + x^5 5 - x^4 4 + x^3 3 - x^2 2…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the polynomial function

f(x)=\frac{x^7}{7}-\frac{x^6}{6}+\frac{x^5}{5}-\frac{x^4}{4}+\frac{x^3}{3}-\frac{x^2}{2}+x

Statement I: The equation

f(x)=0

cannot have two or more roots. Statement II: Rolle's theorem is not applicable to

y=f(x)

on any interval

[a,b]

, where

a,b\in\mathbb{R}