Question
Sun July 29, 2012

Find the intervals in which the function f(x) =x3-6x2+9x+15 is increasing or decreasing

Mon July 30, 2012
Answer : Given : f(x) = x3 - 6x2 +9x +15
To find : the interval in which f(x) is increasing or decreasing

Now
f(x) = x3 - 6x2 +9x +15
f `(x) = 3x2 - 12x + 9 = 3 (x2 - 4x + 3 )

for f(x) to increase
f `(x) > 0
=>  3 (x2 - 4x + 3 ) > 0
=> x2 - 4x + 3  > 0
=> (x - 3) ( x - 1) > 0

+                                                    _                                        +
<----------------------|----------------------|-------------------->
- infinity              1                        3                     + infinity

=>   In the interval -infinity < x < 1  and (union)    3 < x < +infinity f(x) is increasing

and    in the interval  1 < x < 3  , f(x) is decreasing Answer
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