Limits Continuity And Differentiability Question 11
Question: If the mean value theorem is $ f(b)-f(a)=(b-a)f’(c) $ . Then, for the function $ x^{2}-2x+3 $ in $ [ 1,\frac{3}{2} ] $ the value of c is
Options:
A) 6/5
B) 5/4
C) 4/3
D) 7/6
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ f(x)=x^{2}-2x+3 $ .
Since, $ f’(c)=\frac{f( \frac{3}{2} )-f(1)}{\frac{3}{2}-1} $ (given)
$ \Rightarrow 2c-2=\frac{\frac{9}{4}-\frac{6}{2}+3-(1-2+3)}{\frac{3}{2}-1}\Rightarrow c=\frac{5}{4} $
BETA
