Applications Of Derivatives Question 81
Question: Let $ f(x) $ be a function defined as follows: $ f(x)=\sin (x^{2}-3x),x\le 0; $ and $ 6x+5x^{2},x>0 $ Then at $ x=0,f(x) $
Options:
A) Has a local maximum
B)
C) Is discontinuous
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f(0)=\sin 0=0,f({0^{+}})\to {0^{+}} $
$ f({0^{-}})=\underset{x\to {0^{-}}}{\mathop{\lim }},\sin (x^{2}-3x)=\underset{h\to 0}{\mathop{\lim }},\sin (h^{2}+3h)\to {0^{+}} $ Thus, $ f({0^{+}})>f(0) $ and $ f({0^{-}})>f(0) $ .
Hence, $ x=0 $ is a point of minima. Has a local minimum
BETA
