Applications Of Derivatives Question 345
Question: If $ f(x)=2x^{3}-3x^{2}-12x+5 $ and $ x\in [-2,,4] $ , then the maximum value of function is at the following value of x
[MP PET 1987, 2000; Orissa JEE 2005]
Options:
A) 2
B) -1
C) - 2
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ f’(x)=6x^{2}-6x-12 $
$ f’(x)=0\Rightarrow (x-2)(x+1)=0\Rightarrow x=-1,,2 $ Here $ f(4)=128-48-48+5=37 $
$ f(-1)=-2-3+12+5=12 $
$ f(2)=16-12-24+5=-15 $
$ f(-2)=-16-12+24+5=1 $
Therefore the maximum value of function is 37 at $ x=4 $ .
BETA
