For `f(x)={[x^(3),,x<1],[bx^(3),,x>=1]`, LMVT holds on `[0,2]`. The value of `b` and the value of `c` in `(0,2)` is

Statement 1: For the function f(x)=x^(2)+3x+2,LMVT is applicable in [1,2] and the value of c is 3/2. Statement 2: If LMVT is known to be applicable for any quadratic polynomial in [a,b], then c of LMVT is (a+b)/(2) .

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .

The function f(x)=((3^(x)-1)^(2))/(sin x*ln(1+x)),x!=0, is continuous at x=0, Then the value of f(0) is

Let f(x) = x^3 –4x^2 + 8x + 11 , if LMVT is applicable on f(x) in [0, 1], value of c is :

If the function f(x)=2x^(2)+3x+5 satisfies LMVT at x=2 on the closed interval [1,a] then the value of 'a' is equal to

If f(x)=max{x^(2),(1-x)^(2),(3)/(4)},x in[0,1] then the value of of int_(0)^(1)f(x)dx is

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

If the function f(x)=logx, x in [1, e] , satisfies all the conditions of LMVT, then the value of c is