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

Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

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

Let f(x)=e^(2x) and b=a+hdot If there exists a real number theta in (0,1) such that varphi^(prime)(a+thetah)=0 and (e^(2h)-1-2h-2h^2)/(h^3)-A e^(bthetah), then

Verify Rolles theorem for function f(x)=x^2-8x+12 on [2,\ 6]

If f(x)= x^2 , then (f(x+h)-f(x))/(h) =

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)), x in[-2,2],then g(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) = Max. {x^2, (1 - x)^2, 2x(1 - x)} where x in [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

Verify Rolle's theorem for the function f(x)=x^(3)-3x^(2)+2x in the interval [0,2] .

Let f(x)=3x^10-7x^8+5x^6-21x^3+3x^2-7 , then the value of lim_(h->0) (f(1-h)-f(1))/(h^3+3h)

If f(x)=|x-a|varphi(x) , where \ varphi(x) is continuous function, then f'(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f'(a^-) (d) none of these