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).

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) 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(x) = x^(3) and g(x) = 3^(x) . The values of A such that g[f(A)] = f[g(A)] are

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) =

Given f'(1) = 1 and f(2x) = f(x) AA x gt 0 . If f'(x) is differentiable then prove that there exists a number c in (2, 4) such that f''(c) = - 1/8

Let f(x)=(5)/(2)x^(2)-e^(x) . Then the value of c such that f''(c )=0 is s