Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

$x^{3} + 2 x^{2} - 3 x > 0$

The required interval is $(- 3, 0) \cup (1, \infty)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

$x^{3} + 2 x^{2} - 3 x > 0$

This is given to us . we need to solve for x .

Step 2. Factorization

$x (x^{2} + 2 x - 3) > 0 x (x^{2} + 3 x - x - 3) > 0 x (x (x + 3) - 1 (x + 3)) > 0 x (x - 1) (x + 3) > 0$

The zeros of the equation are 0, 1 & -3

Step 3. Dividing the number line into intervals using the above zeros.

The intervals are :

$(- \infty, - 3) (- 3, 0) (0, 1) (1, \infty)$

Step 4. Evaluating the value of function

$1 . (- \infty, - 3) l e t n u m b e r b e - 4 v a l u e o f f u n c t i o n a t - 4 = - 20 c o n d i t i o n n o t s a t i s f i e d . 2 . (- 3, 0) L e t n u m b e r b e - 1 v a l u e o f f u n c t i o n a t - 1 = 4 T h e c o n d i t i o n i s s a t i s f i e d . 3 . (0, 1) l e t n u m b e r b e 0.1 v a l u e o f f u n c t i o n a t 0.1 = - 0.099 c o n d i t i o n n o t s a t i s f i e d . 4 . (0, \infty) L e t n u m b e r b e 2 v a l u e o f f u n c t i o n a t 2 = 10 T h e c o n d i t i o n i s s a t i s f i e d .$

Step 5. conclusion

The required interval is $(- 3, 0) \cup (1, \infty)$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

$x^{3} + 2 x^{2} - 3 x > 0$

Step by Step Solution

Step 1. Given Information

Step 2. Factorization

Step 3. Dividing the number line into intervals using the above zeros.

Step 4. Evaluating the value of function

Step 5. conclusion

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

x3+2x2-3x >0

Step by Step Solution

Step 1. Given Information

Step 2. Factorization

Step 3. Dividing the number line into intervals using the above zeros.

Step 4. Evaluating the value of function

Step 5. conclusion

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$x^{3} + 2 x^{2} - 3 x > 0$