Using Largrange's mean value theorem ...

Using Largrange's mean value theorem
`f(b)-f(a)=(b-a)f'(c )` find the value of c, given `f(x)=x(x-1)(x-2), a=0` and `b=(1)/(2)`.

Verified by Experts

The correct Answer is:

`(1,(sqrt(21))/(6))`

Similar Questions

Explore conceptually related problems

Using Largrange's mean value theorem, prove that, tan^(-1)x lt x

Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt b if f(x)=sqrt(x) and a=4, b=9, find c.

Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt b if f(x)=Ax^(2)+Bx+c" in " a le x le b , find c.

If f(x)=(ax-b)/(bx-a) , then find the value of f(1/x) .

In the mean value theorem f(b)-f(a)=(b-a)f'(c ), (a lt c lt b)," if " f(x)=x^(3)-3x-1 and a=-(11)/(7), b=(13)/(7) , find the value of c.

2f(1/x) - f(x) = 5x , find the value of f(x + 1/x).

In the mean value theorem f(b)-f(a)=(b-a)f'(c )(a lt c lt b) , if a=4, b=9 and f(x)=sqrt(x) , then the value of c is -

if f(x)=mx+c and f(0)=f'(0)=1 then find the value of f(3)

if 2f(x)+3f(-x)=x^2+x+1 find the value of f'(1)

If 2f(x).+ 3f(-x) = x^2-x+1, find the value of f(1).