Applications Of Derivatives Question 274
Question: Let $ f(x)=x^{3}+bx^{2}+cx+d,0<b^{2}<c $ . Then f
[IIT Screening 2004]
Options:
A) Is bounded
B) Has a local maxima
C) Has a local minima
D) Is strictly increasing
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ f(x)=x^{3}+bx^{2}+cx+d $ \ $ f’(x)=3x^{2}+2bx+c $
Now its discriminant $ =4(b^{2}-3c) $
therefore $ 4(b^{2}-c)-8c<0, $ as $ b^{2}<c $ and $ c>0 $
Therefore, $ f’(x)>0 $ for all $ x\in R $
Hence f is strictly increasing.
BETA
