Applications Of Derivatives Question 75
Question: The function $ f:[0,3]\to [1,29], $ defined by $ f(x)=2x^{3}-15x^{2}+36x+1 $ , is
Options:
A) One-one and onto
B) Onto but not one-one
C) One-one but not onto
D) Neither one-one nor onto
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f(x)=2x^{3}-15x^{2}+36x+1 $
$ f’(x)=6x^{2}-30x+36=6(x-2)(x-3) $ Thus, $ f(x) $ is increasing in $ [0,2] $ and decreasing in $ [2,3] $ . Therefore $ f(x) $ is many-one. $ f(0)=1;f(2)=29;f(3)=28 $ Range is $ [1,29] $ .
Hence, $ f(x) $ is many-one-onto.
BETA
