If `f : [-5, 5] to R` is a differentiable function function and if f'(x) does not vanish anywhere, then prove that `f(-5) ne f(5)`.

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is

If f (x) = (x + 1)/(x - 1) is a real function , x ne 1 , then f [f(2)] is . . . .

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')(4) = 1, f(0) = -1 and f^(')(0) = 1 , If g(x) = f(2f^(2)(x)+2))^(2) , then - g^(')(0) equals

If f is the greatest integer function and g is the modulus function, then find the value of (g0f)(-5/3)-(fog)(-5/3)dot