Find the intervals in which the function f (x) is increasing, f (x) = 2x3 - 9x2 + 12x + 15
Asked by Topperlearning User | 6th Aug, 2014, 09:22: AM
Expert Answer:
We have,
f (x) = 2x3 - 9x2 + 12x + 15
& f (x) = 6x2 - 18x + 12 = 6(x2 - 3x + 2)
(i) For f (x) to be increasing, we must have
f'(x) > 0
=> 6 (x2 - 3x + 2) > 0
=> x2 - 3x + 2 > 0 [
6 > 0 \ 6(x2 - 3x + 2) > 0 & x2 - 3x + 2 > 0)
=> (x - 1) (x - 2) > 0
=> x < 1 or x > 2
(¥, 1)υ(2, ¥)
So, f(x) is increasing on (¥, 1)υ(2, ¥)
Answered by | 6th Aug, 2014, 11:22: AM
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