Math Problem Statement

Given the function: 𝑓𝑓(𝑥𝑥) = 1 5 𝑥𝑥5 − 8 3 𝑥𝑥3 + 16𝑥𝑥 (10 Points) a. What are the critical points of f(x)?

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Critical Points
Differentiation
Quadratic Equations

Formulas

f'(x) = x^4 - 8x^2 + 16
Quadratic equation u^2 - 8u + 16 = 0
Quadratic formula: u = [-b ± sqrt(b^2 - 4ac)] / 2a

Theorems

Power Rule for Differentiation
Quadratic Formula

Suitable Grade Level

Grades 11-12, College Calculus