If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < d e, then the minimum number of zeroes of `g(x) = f'(x)^2+f''(x)f(x)` in the interval [a, e] is

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0fora l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d)none of these

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(0) is equals a. 1 b. 0 c. -1 d. none of these

Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')(4) = 1, f(0) = -1 and f^(')(0) = 1 , If g(x) = f(2f^(2)(x)+2))^(2) , then - g^(')(0) equals

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let x = f(t) and y = g(t), where x and y are twice differentiable function If f^(')(0) = g^(')(0) = f^('')(0) = 2, g^(")(0) = 6 , then the value of ((d^(2)y)/(dx^(2))_(t=0) is equal to