Math Problem Statement

Consider the following. f(x) = 5x − 15x1/3 Find f '(x). f '(x) =
Correct: Your answer is correct. Find all critical numbers of f(x). (Enter your answers as a comma-separated list.) x =
Incorrect: Your answer is incorrect. Find all relative extrema of f(x). (If an answer does not exist, enter DNE.) relative maximum (x, y) =

Incorrect: Your answer is incorrect.

relative minimum (x, y) =

Correct: Your answer is correct.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Critical Points
Relative Extrema

Formulas

f'(x) = 5 - 5x^(-2/3)
f'(x) = 0 or undefined to find critical points
Second derivative test or sign analysis for extrema

Theorems

Power Rule
Critical Points Theorem
Relative Extrema Theorem

Suitable Grade Level

Grades 11-12, College Level Calculus