Math Problem Statement

Find the smallest integer a such that the Intermediate Value Theorem guarantees that f(x) = -x^2 + 4x - 1 has a zero on the interval (2, a).

Solution

The problem asks to find the smallest integer ( a \

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Math Problem Analysis

Mathematical Concepts

Intermediate Value Theorem
Quadratic Functions

Formulas

f(x) = -x^2 + 4x - 1

Theorems

Intermediate Value Theorem

Suitable Grade Level

Grades 10-12