If the mean value theorem is f'(c)=f(b)-f(a)b-a. Then, for the function x2-2x+3 in 1,32, the value of c is.
65
54
43
76
Explanation of the correct option.
Compute the required value.
Given : f(x)=x2-2x+3
Differentiate the function with respect to x,
f'(x)=2x-2⇒f'(c)=2c-2
Since,
f'(c)=f(b)-f(a)b-a⇒2c-2=f32-f132-1⇒2c-2=94-3+3-1+2-112⇒2c-2=322-232+3-1+2-312⇒2c-2=12⇒2c=52⇒c=54
Hence option B is the correct option.
If the mean value theorem is f(b)-f(a)=(b-a)f'(c). Then for the function x2-2x+3 in 1,32, the value of c is