Applications Of Derivatives Question 410
Question: In the mean value theorem, $ f(b)-f(a)=(b-a)f’(c) $ if $ a=4 $ , $ b=9 $ and $ f(x)=\sqrt{x} $ then the value of c is
[J & K 2005]
Options:
A) 8.00
B) 5.25
C) 4.00
D) 6.25
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\sqrt{x} $
$ \therefore f(a)=\sqrt{4}=2, $
$ f(b)=\sqrt{9}=3 $ ; $ {f}’(x)=\frac{1}{2\sqrt{x}} $ Also, $ {f}’(c)=\frac{f(b)-f(a)}{b-a}=\frac{3-2}{9-4}=\frac{1}{5} $
$ \therefore $ $ \frac{1}{2\sqrt{c}}=\frac{1}{5} $
therefore $ c=\frac{25}{4}=6.25 $ .
BETA
