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

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___

If f(2)=2a n df^(prime)(2)=1, then find (lim)_(xvec2)(xf(2)-2f(x))/(x-2)

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=5 , find f(x) .

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

If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , write the value of (dy)/(dx) at x=0 .