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Unformatted text preview: Lecture 18: Section 2.7 Nonlinear Inequalities To Solve a Polynomial Inequality 1. Write the inequality with 0 on the right hand side to obtain one of the following: u1D453 ( u1D465 ) > u1D453 ( u1D465 ) u1D453 ( u1D465 ) < u1D453 ( u1D465 ) 2. Find all real zeros of the polynomial u1D453 ( u1D465 ). These zeros are the critical numbers of u1D453 ( u1D465 ). 3. Use the critical numbers to determine the test intervals. 4. Choose a number in each interval and evaluate u1D453 at the number. a) If the function value is positive, then u1D453 ( u1D465 ) > for all numbers u1D465 in the interval. b) If the function value is negative, then u1D453 ( u1D465 ) < for all numbers u1D465 in the interval. 5. Include endpoints if u1D453 ( u1D465 ) 0 or if u1D453 ( u1D465 ) 0. FACT: A polynomial changes signs only at its zeros. Between two zeros, a polynomial must be entirely positive or entirely negative....
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This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.
 Summer '08
 GERMAN
 Calculus, Inequalities

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