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

Let f(x+y)=f(x).f(y) for all x and y suppose f(5)=2 and f'(0)=3. Find f'(5) .

Let f(x+y) = f(x).f(y), forall, x, y . Suppose f(5) =2, f^(')(0) = 3 then f^(')(5) =

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 f(x) is positive for all real x f(x) is negative for all real x f(x)=0 has real roots Nothing can be said about the sign of f(x)

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

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

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)=cosalpha, then prove that f(x)>0AAx in Rdot