Math Problem Statement

Find the intervals on which the function is increasing and decreasing, identify critical points, and evaluate integrals for the given calculus problems.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Critical Points
Increasing and Decreasing Functions
Integration (Indefinite and Definite)

Formulas

Derivative: f'(x) = dy/dx
Critical Points: f'(x) = 0 or undefined
Integration by substitution
Definite Integral: ∫[a, b] f(x) dx

Theorems

Fundamental Theorem of Calculus
First Derivative Test
Second Derivative Test

Suitable Grade Level

Undergraduate Calculus Level

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