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:

f(x)=x3+3xx1f(x) = \frac{x^3 + 3x}{x - 1}

And the question is asking which of the following is the smallest value for bab - a, where aa and bb are values for which the function is evaluated at two different points.

The provided options are:

  1. 2
  2. 4
  3. 6
  4. 8

Let me know if you'd like further clarification or help solving the problem!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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