Applications Of Derivatives Question 4
Question: Consider the following statements:
- $ f(x)= $ ln x is an increasing function on $ ( 0,\infty ). $
- $ f(x)=e^{x}-x(lnx) $ is an increasing function on $ ( 1,,\infty ) $ . Which of the above statements is/are correct-
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x)=\log ,x $ Clearly $ f(x) $ is increasing on $ (0,\infty ) $
$ f(x)=e^{x}-x\log x $
$ f’(x)=e^{x}-(\log ,x+1) $ From the figure it is clear that $ f’(x)>0 $ on $ (1,\infty ) $ . So both statements (1) & (2) are correct.
BETA
