CBSE Class 12-science Answered
Find the intervals in which the function f(x) =x3-6x2+9x+15 is increasing or decreasing
Asked by Gurpreet Kaur | 29 Jul, 2012, 11:29: AM
Expert Answer
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
Answered by | 30 Jul, 2012, 02:05: AM
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