Math Problem Statement

Question content area top Part 1 Use the derivative f prime to determine the local minima and maxima of f and the intervals of increase and decrease. Sketch a possible graph of f​ (f is not​ unique). f prime​(x)equals30 sine 3 x on left bracket negative StartFraction 4 pi Over 3 EndFraction comma StartFraction 4 pi Over 3 EndFraction right bracket Question content area bottom Part 1 The local​ minimum/minima is/are at xequals    enter your response here. ​(Use a comma to separate answers as needed. Type an exact​ answer, using pi as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Critical Points
Trigonometric Functions
Sine Function

Formulas

f'(x) = 30 sin(3x)
Critical points: f'(x) = 0
Increasing/Decreasing intervals: f'(x) > 0 or f'(x) < 0

Theorems

Critical Point Theorem
First Derivative Test
Sine Function Properties

Suitable Grade Level

Undergraduate (Calculus I or II)