Math Problem Statement

Find all points on the graph of the function f(x) = 2 sin(x) + sin2(x) at which the tangent line is horizontal. (Use n as your arbitrary integer.) (x, y)

Incorrect: Your answer is incorrect.

(smaller y-value) (x, y)

Incorrect: Your answer is incorrect.

(larger y-value)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometric Functions
Horizontal Tangents

Formulas

f'(x) = 2cos(x) + 2sin(x)cos(x)
cos(x) = 0 implies x = π/2 + nπ
1 + sin(x) = 0 implies sin(x) = -1

Theorems

Derivative of Trigonometric Functions
Chain Rule
Critical Points

Suitable Grade Level

Grades 11-12, College Calculus