Math Problem Statement

Show that the equation has three unique solutions by using the following steps: i. Define a function that has zeros whenever the given equation has a solution. ii. Provide a plot of the graph and indicate approximate locations of three of the function’s zeros. (desmos.com might be helpful for this!) iii. Use the Intermediate Value Theorem to show that there actually is three zeros near the ones you found by plotting. Make sure you verify all necessary conditions for the Intermediate Value Theorm to apply. x tan(x) = 2 x − x 2 3 f (x) y = f (x)

Solution

We are given the equation:

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Math Problem Analysis

Mathematical Concepts

Algebra
Trigonometry
Intermediate Value Theorem
Graphing

Formulas

x tan(x) = 2x - x^2 / 3

Theorems

Intermediate Value Theorem

Suitable Grade Level

Grades 11-12