Math Problem Statement

  1. What are the critical values of f(x)?
  2. On what intervals is f increasing?
  3. On what intervals is f decreasing?
  4. Find the x values of the local maxima 5. Find the x values of the local minima

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Critical Points
First Derivative
Increasing/Decreasing Functions
Local Maxima/Minima

Formulas

f'(x) = 0 for critical points
f'(x) > 0 for increasing intervals
f'(x) < 0 for decreasing intervals

Theorems

First Derivative Test

Suitable Grade Level

Grades 11-12