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