Math Problem Statement

Let f(x) = 15x + 5/x . (a) Find the interval(s) where f(x) is increasing. (Enter your answer using interval notation.)

Correct: Your answer is correct. (b) Find the interval(s) where f(x) is decreasing. (Enter your answer using interval notation.)

Incorrect: Your answer is incorrect. (c) Find the x-value(s) of all local maxima of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x =

Incorrect with credit: Your answer is incorrect, but you received credit for a previous answer. (d) Find the x-value(s) of all local minima of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x =

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Critical Points
Increasing/Decreasing Functions

Formulas

f'(x) = 15 - 5/x^2 (first derivative of f(x))
Critical points: f'(x) = 0

Theorems

First Derivative Test
Local Maxima and Minima

Suitable Grade Level

Grade 11-12 (High School Calculus)