Math Problem Statement

The function sin cos 4 4 x x + is increasing in the interval

Solution

To determine the interval where the function f(x)=sin⁡(x)+cos⁡(x)+4xf(x) = \sin(x) + \cos(x) + 4x is increasing, we need to find where the derivative of the function is positive. The function increases when the first derivative is greater than zero

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometric Functions
Derivatives
Increasing Functions

Formulas

f(x) = sin(x) + cos(x) + 4x
f'(x) = cos(x) - sin(x) + 4

Theorems

First Derivative Test

Suitable Grade Level

Grades 11-12 or Early College

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