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 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)

If f(x)=|cosx-sinx| ,find f^(prime)(pi/6) and f^(prime)(pi/3)dot

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

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, the prove that f(x)>0AAx in Rdot

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, the prove that f(x)>0AAx in Rdot

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, the prove that f(x)>0AAx in Rdot

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

If f((x+y)/3)=(2+f(x)+f(y))/3 for all real xa n dy and f^(prime)(2)=2, then determine y=f(x)dot

If f((x+y)/3)=(2+f(x)+f(y))/3 for all real xa n dy and f^(prime)(2)=2, then determine y=f(x)dot