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dulce129
29.11.2020 •
Mathematics
Identify the interval(s) on which the function y = -x2 + 5x + 14 is positive.
A.) X < -2 and x > 7
B.) X > 2 and x < -7
C.) -7 < x < 2
D.) -2 < x < 7
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Ответ:
Given:
To find:
The interval on which the given function is positive.
Solution:
We have,
Splitting the middle term, we get
Using zero product property, we get
-2 and 7 divide the number line is three interval.
Interval Signs of
Result
(-∞,-2) (-)(-)(-) Negative
(-2,7) (-)(-)(+) Positive
(7,∞) (-)(+)(+) Negative
So, the function is positive for the interval (-2,7), i.e., -2 < x < 7.
Therefore, the correct option is D.
Ответ:
The median side