Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If  \mathrm{f(x)=|x-a| \phi(x)} , where \mathrm{\phi(x)}  is continuous function, then

Option: 1

\mathrm{f^{\prime}\left(a^{+}\right)=\phi(a)}


Option: 2

f^{\prime}\left(a^{-}\right)=+\phi(a)


Option: 3

\mathrm{f^{\prime}\left(a^{+}\right)=f^{\prime}\left(a^{-}\right)}


Option: 4

none of these


Answers (1)

best_answer

\mathrm{ \text { sotution: } f^{\prime}\left(a^*\right)=\lim _{x \rightarrow a^{+}} \frac{f(x)-f(0)}{x-a}=\lim _{x \rightarrow a^{+}} \frac{|x-a| \phi(x)}{x-a} \\ }

\mathrm{ =\lim _{x \rightarrow a} \frac{(x-a)}{(x-a)} \alpha(x)[\because x>a \therefore|x-a|=x-a] \\ }

\mathrm{=\lim _{x \rightarrow \infty} 0(x) \\ }

\mathrm{ =\varphi(a) \quad[\because \bullet(x) \text { is continuous at } x=a] \\ }
and 
\mathrm{ f^{\prime}\left(a^{-}\right) =\lim _{x \rightarrow a^{-}} \frac{f(x)-f(0)}{x-a}=\lim _{x \rightarrow a^{-}} \frac{|x-a| \phi(x)}{x-a} \\ }
\mathrm{ =-\lim _{x \rightarrow a} \frac{(x-a) \phi(x)}{(x-a)} \quad[\because x<a \therefore|x-a|=-(x-a)] \\ }
\mathrm{ =-\lim _{x \rightarrow a} \emptyset(x) \\ }
\mathrm{ =-0(a) \quad \quad[\because \bullet(x) \text { is continuous at } x=a] }
 

Posted by

Suraj Bhandari

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Marks vs Percentile 2025: How many marks do you need to score 95+ percentile?
anam-khan

JEE Main 2025 session 1 official answer key out; challenge by February 6; how to calculate NTA score?
anam-khan

JEE Main 2025: NIT Raipur's CSE cut-offs drop; closing ranks in popular branches

Latest Question