[" In the mean value theorem,"f(x+h)=f(x)+hf'(x+theta h)],[(0

Show that the value of theta in the mean value theorem f(x+h)=f(x)+hf'(x +theta h) is independent of x if f(x)=a+bx+cm^(x) .

In the mean value theorem, f(a+h)=f(a)+hf'(a+theta h) (0 lt theta lt 1), find theta when f(x)=sqrt(x), a=1 and h=3.

In the mean value theorem f(a+h)=f(a)+hf'(a+theta h) ( 0 lt theta lt 1) , if f(x)=sqrt(x), a=1, h=3 , then the value of theta is -

Compute the value of theta the first mean value theorem f(x+h) =f(x) + hf'(x+theta h) if f(x) = ax^(2) + bx + c

If f(x)=Ax^(2)+Bx+C and A ne 0 then find the value of theta in Lagrange's mean value theorem, f(x+h)=f(x)+h f'(x+theta h) .

In the following Lagrange's mean value theorem, f(a+h)-f(a)=hf'(a+theta h), 0 lt theta lt 1 If f(x)=(1)/(3) x^(3)-(3)/(2) x^(2)+2x, a=0 and h=3 " find " theta .

Find 'c' of the mean value theorem, if: f(x) = x(x-1) (x-2), a=0, b=1//2

The value of ′c′ in Lagrange's mean value theorem for f(x) = x(x−2)2 in [0,2] is-

The value of ′c′ in Lagrange's mean value theorem for f(x) = x(x−2)^2 in [0,2] is-