Functions Question 352
Question: Let $ f $ be differentiable for all $ x $ . If $ f(1)=-2 $ and $ f’(x)\ge 2 $ for $ x\in
[1,6] $ , then [AIEEE 2005]
Options:
A) $ f(6)<5 $
B) $ f(6)=5 $
C) $ f(6)\ge 8 $
D) $ f(6)<8 $
Show Answer
Answer:
Correct Answer: C
Solution:
As $ f(1)=-2 $ and $ f’(x)\ge 2\forall x\in [1,6] $ Applying lagrange?s mean value theorem, $ \frac{f(6)-f(1)}{5} $ $ =f’(c)\ge 2 $
$ \Rightarrow f(6)\ge 10+f(1)\Rightarrow f(6)\ge 10-2\Rightarrow f(6)\ge 8 $ .
BETA
