Applications Of Derivatives Question 201
Question: If f(x) and g(x) are differentiable functions for $ 0\le x\le 1 $ such that f(0)=10, g(0)=2, f(1)=2, g(1)=4, then in the interval (0, 1),
Options:
A) f’(x) =0 for all x
B) f’(x)+4g’(x)=0 for at least one x
C) f’(x)=2g’(x) for at most done x
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] We know that there exists at least one x in (0, 1) for which $ \frac{f(1)-f(0)}{g(1)-g(0)}=\frac{f’(x)}{g’(x)} $ Or
$ \frac{2-10}{4-2}=\frac{f’(x)}{g’(x)} $ or $ f’(x)+4g’(x)=0 $ For at least one x in (0, 1).
BETA
