Applications Of Derivatives Question 96
Question: If $ f(x)=2x^{3}-21x^{2}+36x-30 $ , then which one of the following is correct
Options:
A) $ f(x) $ has minimum at $ x=1 $
B) $ f(x) $ has maximum at $ x=6 $
C) $ f(x) $ has maximum at $ x=1 $
D) $ f(x) $ has no maxima or minima
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=2x^{3}-21x^{2}+36x-30\Rightarrow f’(x)=6x^{2}-42x+36 $
$ \therefore f’(x)=0\Rightarrow x=6,\ 1 $ and $ {f}’’,(x)=12x-42 $ Here $ {f}’’,(1)=-30 $ and $ {f}’’,(6)=30 $
Hence $ f(x) $ has maxima at $ x=1 $ and minima at $ x=6 $ .
BETA
