Let f(x) is differentiable function in [2, 5] such that `f(2)=(1)/(5)` and `f(5)=(1)/(2)`, then the exists a number `c, 2 lt c lt 5` for which f '(c) equals :-

If f(x) is differentiable in the interval [2,5] , where f(2) = ( 1)/(5) and f(5) = ( 1)/(2), then there exists a number 2 lt c lt 5 for which f(c ) is equal to

f(x) and g(x) are differentiable functions for 0 le x le 2 such that f(0)=5, g(0)=0, f(2)=8, g(2)=1 . Show that there exists a number c satisfying 0 lt c lt 2 and f'(c)=3g'(c) .

f(x) and g(x) are differentiable functions for 0 <= x <= 2 such that f(0) = 5, g(0) = 0, f(2)= 8,g(2) = 1. Show that there exists a number c satisfying 0 < c < 2 and f'(c)=3 g'(c).

Let f(x) be a differentiable function in [2, 7] . If f(2) = 3 and f'(x) lt= 5 for all x in (2, 7), then the maximum possible value of f (x) at x=7 is

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(xrarr2)(f(4)-f(x^2))/(x-2) equals

Let f(x) and g(x) be differentiable functions for 0 le x le 1 such that f(0) = 2, g(0) = 0, f(1) = 6 . Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =

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

Let f (x) and g (x) be two differentiable functions for 0 le x le 1 such that f (0) = 2, g (0) = 0,f (1) = 6. If there exists a real number c in (0,1) such that f'(c ) = 2 g '(c ) , then g (1) is equal to