Applications Of Derivatives Question 239
Question: The function $ f(x)=x^{3}-3x^{2}-24x+5 $ is an increasing function in the interval given below
[MP PET 1998]
Options:
A) $ (-\infty ,,-2)\cup (4,\infty ) $
B) $ (-2,\infty ) $
C) (-2, 4)
D) $ (-\infty ,,4) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=x^{3}-3x^{2}-24x+5 $ For increasing, $ f’(x)>0 $ , $ 3x^{2}-6x-24>0 $
therefore $ x^{2}-2x-8>0 $
$ x^{2}-4x+2x-8>0 $
therefore $ (x+2)(x-4)>0 $
$ x\in (-\infty ,,-2)\cup (4,\infty ) $ .
BETA
