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(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

If f(x) is a twice differentiable function and given that f(1)=2,f(2)=5 and f(3)=10 then

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these

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 and f(1)=1, then

If f(x) is differentiable function such that int_0^xf(t)dt=((f(x))^2)/2 for all x and f(2)!=0, then value of f ' (2) is a. 3 b. 1 c. 2 d. -1 e. -2

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

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

If f:RrarrR,f(x) is a differentiable function such that (f(x))^(2)=e^(2)+int_(0)^(x)(f(t)^(2)+(f'(t))^(2))dtAAx inR . The values f(1) can take is/are

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........