Request a call back

# CBSE Class 12-science Answered

Find the intervals in which the function f (x) is  decreasing f(x) = 2x3 + 9x2 + 12x + 20

Asked by Topperlearning User | 06 Aug, 2014, 09:29: AM Expert Answer

We have,

f (x) = 2x3 + 9x2 + 12x + 20

\ 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 and 6 (x2 + 3x + 2) > 0 \ x2 + 3x + 2 > 0]

=> (x + 1) (x + 2) > 0

=> x < -2 or x > -1

Therefore, (-¥, -2) & (-1, ¥)

So, f (x) is increasing on (¥, -2) & (-1, ¥)

(ii)   for f (x) to be decreasing, we must have

f ' (x) < 0

=> 6(x2 + 3x + 2) < 0

=> x2 + 3x + 2 < 0          [ 6 > 0 and 6(x2 + 3x + 2) < 0 \ x2 + 3x + 2 < 0]

=> (x + 1)(x + 2) < 0

-2 < x < -1

So, f (x) is decreasing on (-2, -1)

Answered by | 06 Aug, 2014, 11:29: AM

## Concept Videos

CBSE 12-science - Maths
Asked by haroonrashidgkp | 08 Sep, 2018, 04:16: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 08:00: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 08:12: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 09:18: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 09:20: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 09:22: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 09:29: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 09:54: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 10:12: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 06 Aug, 2014, 10:17: AM ANSWERED BY EXPERT