If f and g are differentiable functions in [0, 1] satisfying `f(0)""=""2""=g(1),g(0)""=""0` and `f(1)""=""6` , then for some `c in ]0,""1[` (1) `2f^'(c)""=g^'(c)` (2) `2f^'(c)""=""3g^'(c)` (3) `f^'(c)""=g^'(c)` (4) `f'(c)""=""2g'(c)`

If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(0)=2,g(0) = 0,f(1)=6,g(1)=2 , then in the interval (0,1)

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

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) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6, f(2)=3, g(2)=9, then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0)=0,f(1)=6a n dg(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

Let f and g be two differentiable functions on R such that f'(x)>0 and g′(x) g(f(x-1)) (b) f(g(x))>f(g(x+1)) (c) g(f(x+1))

Let f:""(-1,""1) rarr R be a differentiable function with f(0)""=""-1" "a n d" "f'(0)""=""1 . Let g(x)""=""[f(2f(x)""+""2)]^2 . Then g'(0)""= (1) -4 (2) 0 (3) 2 (4) 4

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these