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
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