Statement 1: The greatest of the numbers is

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Statement 1: The greatest of the numbers 313,414,515,6163^{\frac{1}{3}}, 4^{\frac{1}{4}}, 5^{\frac{1}{5}}, 6^{\frac{1}{6}} is 3133^{\frac{1}{3}}. Statement 2: The function f(x)=(1x)xf(x) = \left(\frac{1}{x}\right)^x is strictly increasing for 0<x<1e0 < x < \frac{1}{e}. (a) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (b) Statement-1 is true statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (c) Statement-1 is true, statement-2 is false. (d) Statement-1 is false, statement-2 is true.

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