Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The graph of function f contains the point P(1,2), and Q(s, r). The equation of the secant line through P and Q is<img alt="\mathrm{ y=\frac{\left(s^2+2 s-3\right)}{(s-1)} x-1-s. The\, \, value \,

The graph of function f contains the point P(1,2), and Q(s, r). The equation of the secant line through P and Q is\mathrm{ y=\frac{\left(s^2+2 s-3\right)}{(s-1)} x-1-s. The\, \, value \, \, of \, \, f^{\prime}(1)\, \, is : }
 

Option: 1

2


Option: 2

3


Option: 3

4


Option: 4

does not exist


Answers (1)

best_answer

 Method I : By definition \mathrm{ f^{\prime}(1) } is the limit of the slope of the secant line when \mathrm{ s \rightarrow 1. }
Thus,
\mathrm{ \begin{aligned} f^{\prime}(1) & =\lim _{s \rightarrow 1} \frac{s^2+2 s-3}{s-1} \\ & =\lim _{s \rightarrow 1} \frac{(s-1)(s+3)}{(s-1)}=4 \end{aligned} }
Method II : By substituting x=s into the equation of the secant line and cancelling (s-1) again, we get derivative is \mathrm{ f^{\prime}(s)=2 s+2 so, f^{\prime}(1)=4. }.

Posted by

Rishi

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

Andhra launches free JEE, NEET coaching to over 1 lakh govt school students
anam-khan

JoSAA Counselling 2025 LIVE: BTech registration starts at josaa.nic.in for IIT, NIT, IIIT admissions
anam-khan

Kota: 17-year old student from UP preparing for JEE dies of electrocution in hostel

Latest Question