Math Problem Statement
تابع f(x) = (x^3 + 3x) / (x - 1) در بازه (a,b) اکیداً نزولی است. بیشترین مقدار b - a کدام است؟ گزینهها: 1) 2، 2) 4، 3) 6، 4) 8
Solution
The image you uploaded contains a mathematical problem in Persian. Here's a translation and breakdown of the content:
Problem:
We are given the following function:
And the question is asking which of the following is the smallest value for , where and are values for which the function is evaluated at two different points.
The provided options are:
- 2
- 4
- 6
- 8
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Math Problem Analysis
Mathematical Concepts
Calculus
Monotonicity
Intervals
Formulas
f'(x) = derivative of (x^3 + 3x) / (x - 1)
Theorems
Monotonicity test using first derivative
Critical points analysis
Suitable Grade Level
Grades 11-12