Let `f(x+y)=f(x)dotf(y)` for all `xa n dydot` Suppose `f(5)=2a n df^(prime)(0)=3.` Find `f^(prime)(5)dot`

Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then (a) f(x) is positive for all real x (b) f(x) is negative for all real x (c) f(x)=0 has real roots (d)Nothing can be said about the sign of f(x)

Let f(x+y)=f(x)+f(y)+2x y-1 for all real xa n dy and f(x) be a differentiable function. If f^(prime)(0)=sinalpha, the prove that f(x)>0AAx in Rdot

If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) will be

If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 , find f'(5).

Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3fora l lx ,y in Rdot If f^(prime)(0)geq0, find f(10)dot

Let f(x+y)=f(x)+f(y)+2x y-1 for all real x and y and f(x) be a differentiable function. If f^(prime)(0)=cosalpha, the prove that f(x)>0AAx in Rdot

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(5)) .

Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

If f(x+y+z)=f(x) f(y) f(z) ne 0 for all x,y,z and f(2)=5, f'(0)=2, find f'(2).

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)