Applications Of Derivatives Question 18
Question: The function $ y=2x^{3}-9x^{2}+12x-6 $ is monotonic decreasing, when
[MP PET 1994]
Options:
A) $ 1<x<2 $
B) $ x>2 $
C) $ x<1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ f(x)=y=2x^{3}-9x^{2}+12x-6 $
$ \Rightarrow $ $ f’(x)=6x^{2}-18x+12 $
Since $ f(x) $ is increasing or decreasing in $ (a,b) $ according as $ f’(x)>0 $ or $ <0 $ for every $ x\in (a,b) $ .
Hence $ f’(x)=6(x-2)(x-1) $ which is obviously decreasing if $ x\in (1,2),i.e.,,1<x<2 $ .
BETA
