Applications Of Derivatives Question 237
Question: The interval of the decreasing function $ f(x)=x^{3}-x^{2}-x-4 $ is
Options:
A) $ ( \frac{1}{3},,1 ) $
B) $ ( -\frac{1}{3},1 ) $
C) $ ( -\frac{1}{3},,\frac{1}{3} ) $
D) $ ( -1,-\frac{1}{3} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ f(x)=x^{3}-x^{2}-x-4 $ This function will be decreasing function when $ f’(x)<0 $
therefore $ 3x^{2}-2x-1<0\Rightarrow 3x^{2}-3x+x-1<0 $
therefore $ (3x+1)(x-1)<0 $ ;
$ \therefore 3x+1>0 $ and $ x-1<0 $
$ x>-\frac{1}{3} $ and $ x<1 $ : $ \therefore x\in ( \frac{-1}{3},,1 ) $ .
BETA
