Let `f(x)=x^4-6x^3+12 x^2-8x+3.` If Rolles theorem is applicable to `varphi(x)` on `[2,2+h]` and there exist `c in (2,2+h)` such that `varphi^(prime)(c)=0` and `(f(2+h)-f(2))/(h^3)=g(c),` then

Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

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

Let f(x)={(x^(a) , x > 0),(0, x=0):} .Rolle's theorem is applicable to f for x in[0,1] ,if a : (A) -2 (B) -1 (C) 0 (D) (1)/(2)

Let f(x)=4x^3-3x^2-2x+1, use Rolles theorem to prove that there exist c ,\ 0

Let Rolle's theorem is applicable for f(x)=x^(3)+ax^(2)+beta x+2 where x in[0,2] and the value of c= (1)/(2) then (a+2 beta) is

Let f(x)=Max .{x^(2),(1-x)^(2),2x(1-x)}wherexin[0,1] If Rolle's theorem is applicable for f(x) on largestpossible interval [a,b] then the value of 2(a+b+c) when c in[a,b] such that f(c)=0, is

Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot

Let f(x) and g(x) be differentiable for 0<=x<=2 such that f(0)=2,g(0)=1, and f(2)=8. Let there exist a real number c in [0,2] such that f'(c)=3g'(c). Then find the value of g(2)

If f(x) is differentiable at x=a and f^(prime)(a)=1/4dot Find (lim)_(h->0)(f(a+2h^2)-f(a-2h^2))/(h^2)