Let `f(x)a n dg(x)` be two differentiable functions in `Ra n df(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8.` Then prove that `g^(prime)(x)=4f^(prime)(x)` for at least one `x in (2,4)dot`

Let f(x)and g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 , g'(1)=6 , f(2)=3 and g(2)=9 . Then what is f(x)-g(x) at x=4 equal to ?

f(x) and g(x) are two differentiable functions in [0,2] such that f(x)=g(x)=0,f'(1)=2,g'(1)=4,f(2)=3,g(2)=9 then f(x)-g(x) at x=(3)/(2) is

f(x) and g(x) are two differentiable functions in [0,2] such that f(x)=g(x)=0,f'(1)=2,g'(1)=4,f(2)=3,g(2)=9 then f(x)-g(x) at x=(3)/(2) is

If f(x) and g(x) are differentiable functions for 0<=x<=1 such that f(0)=10,g(0)=2,f(1)=2,g(1)=4 then in the interval (0,1).f'(x)=0 for all xf'(x)+4g'(x)=0 for at least one xf(x)=2g'(x) for at most one x none of these

LEt f(x) be a differentiable function and f'(4)=5. Then,lim_(x rarr2)(f(4)-f(x^(2)))/(x-2) equals

If f(x),g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x)f'(1)=2g'(1)=4 and f(2)=3g(2)=9 then f(x)-g(x) at x=4 equals (A) 0 (B) 10 (C) 8 (D) 2

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