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

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 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)a n dg(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(x)a n dg(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 an even function and f'(x) exists, then f'(0) is

Let f be an even function and f'(x) exists, then f'(0) 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))