Let `f(x)` be a nonzero function whose all successive derivative exist and are nonzero. If `f(x), f' (x) and f''(x)` are in G.P. and `f (0) = 1, f '(0) = 1`, then -

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f be a real function such that f(x-y), f(x)f(y) and f(x+y) are in A.P. for all x,y, inR. If f(0)ne0, then

f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If f'(x) ne 0 , then maximum number of real roots of f''(x) = 0 is /are

Let f(x) be polynomial function of defree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

Let f(x) be a differentiable function for all x in R The derivative of f(x) is an even function If the period of f(2x) is 1 then the value of f(2)+f(4)-f(6)-f(8) is.

Let f(x) and g(x) be two function having finite nonzero third-order derivatives f''(x) and g''(x) for all x in R. If f(x)g(x)=1 for all x in R, then prove that (f''')/(f')-(g'')/(g')=3((f'')/(f)-(g'')/(g))

Let f be a function such that f(x)>0 Assume that f has derivatives of all orders and that In f(x)=f(x)int_(0)^(x)f(t)dt find f^(2)(0)