Functions Question 462
Question: If $ f(x)=x^{2}-2x+4 $ and $ \frac{f(5)-f(1)}{5-1}=f’(c) $ then value of c will be
[AMU 2005]
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=x^{2}-2x+4 $ ; $ f’(x)=2x-2 $ At $ x=c $ , $ f’(c)=2c-2 $ $ f(5)=5^{2}-2(5)+4=19 $ ; $ f(1)=1^{2}-2(1)+4=3 $ $ \frac{f(5)-f(1)}{5-1}=f(c) $
Þ $ \frac{19-3}{5-1}=2c-2 $
Þ $ \frac{16}{4}=2c-2 $
Þ $ 4=2c-2 $
Þ $ 2c=6 $ or $ c=3 $ .
BETA
