Let f(x) and g(x) be two differentiable functions in R and f(2) = 8, g(2) = 0, f(4) = 10, and g(4) = 8. Then prove that g'(x) = 4 f'(x) for at least one `x in (2, 4)`.

Let f and g be differentiable functions such that f(3) = 5, g(3) = 7, f'(3) = 13, g'(3) = 6, f'(7) = 2 and g'(7) = 0 . If h(x) = (fog)(x) , then h'(3) =

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

Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x), g'(x) be a, b, respectively, (a lt b) . Show that there exists at least one root of equation f'(x) g'(x) + f(x) g''(x) = "0 on" (a, b) .

Let f(x) and g(x) be differentiable for 0 le x le 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).

Find f o g and g o f f(x) = |x| and g(x) = |5x -2|

Let f and g be two functions defined by f(x)=sqrt(x-1) ,and g(x)=sqrt(4-x^2) .Find f-g

Let f and g be two functions defined by f(x)=sqrt(x-1) ,and g(x)=sqrt(4-x^2) .Find f/g