1 2 7 correct 2 0 2 7 7 3 0 2 7 4 7 5 0 0 2 7

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1. (2 , 7) correct 2. ( -∞ , 0) (2 , 7) (7 , ) 3. ( -∞ , 0) (2 , 7) 4. (7 , ) 5. ( -∞ , 0) (0 , 2) (7 , ) Explanation: Because of the property of derivatives, we know that y will be decreasing when y is negative. Let us first solve for the constant solutions to this equation. A constant solution to a differential equation is a solution where y is constant, hence where y = 0. So in this case y = y 4 - 9 y 3 + 14 y 2 = y 2 ( y 2 - 9 y + 14 ) = y 2 ( y - 2)( y - 7) . Hence y = 0 if and only if y = 0 , 2 , 7. This divides the real number line into 4 intervals: ( -∞ , 0) , (0 , 2) , (2 , 7) , (7 , ) . By computing y for some value of y in each interval, we can see that y is negative on the interval (2 , 7) .

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