Let `fa n dg` be differentiable on `R` and suppose `f(0)=g(0)a n df^(prime)(x)lt=g^(prime)(x)` for all `xgeq0.` Then show that `f(x)lt=g(x)` for all `xgeq0.`

Let f(x) and g(x) be two functions which are defined and differentiable for all x>=x_(0). If f(x_(0))=g(x_(0)) and f'(x)>g'(x) for all x>x_(0), then prove that f(x)>g(x) for all x>x_(0).

Iff (x) and g(x) be two function which are defined and differentiable for all x>=x_(0). If f(x_(0))=g(x_(0)) and f'(x)>g'(x) for all f>x_(0), then prove that f(x)>g(x) for all x>x_(0).

Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=3 , find f^(prime)(5) .

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is

Let f : R to R be differentiable at c in R and f(c ) = 0 . If g(x) = |f(x) |, then at x = c, g is

If f'(x)=(1)/(1+x^(2)) for all x and f(0)=0 , show that 0.4 lt f (2) lt2

Let F : R to R be a thrice differentiable function . Suppose that F(1)=0,F(3)=-4 and F(x) lt 0 " for all" x in (1,3). f(x) = x F(x) for all x inR . The correct statement (s) is / are

If f and g are differentiable at a in R such that f(a)=g(a)=0 and g'(a)!=0 then show that lim_(x rarr a)(f(x))/(g(x))=(f'(a))/(g'(a))