Calculus problem, look below
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Calculus problem, look below

[From: ] [author: ] [Date: 12-11-19] [Hit: ]
.....a*b+.......

the product of two numbers is negative only if one is positive and one negative


a... b......a*b
+....+........+
+....-.........-
-.....+.......-
-.....-........+

when the signs are the same the product is positive ... so the only way it can be negative on the interval that each factor is different sign..

(x +8)(x - 5) < 0

(x + 8) < 0 when x < -8

(x + 8) > 0 when x > -8

(x - 5) < 0 when x < 5

(x -5 ) > 0 when x > 5


x < -8 and x > 5 impossible

or

x > -8 and x < 5 happens when -8 < x < 5

so f(x) is decreasing on the interval is ( -8, 5)

use open brackets because the -8 and 5 are not in the answer

===============

the f function is increasing when both signs are the same

(x + 8) < 0 when x < -8

(x + 8) > 0 when x > -8

(x - 5) < 0 when x < 5

(x -5 ) > 0 when x > 5


x < -8 and x < 5
this means x < -8 makes both equations true
so the interval is (- inf , -8)

or

x > -8 and x > 5
x > 5 makes both equations true
this interval is ( 5 , infinity)

thats how you solve all those equations


================

remember when BOTH inequalities have to be a certain value you have to use the LOGIC AND

THAT is why i said x>8 and x > -5 had to be true..

since anything x>8 makes both of these true that is the simple formula... for that combined one..
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