Let `f: R ->R` be a differentiable and strictly decreasing function such that `f(0)=1` and `f(1)=0`. For `x in R`, let `F(x)=int _0^x(t-2)f(t)dt`

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 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 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 f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f:R rarr R be a differentiable function such that its derivative f 'is continuous and f(pi)=-6. If F:[0,1]rarr R is defined by F(x)=int_(0)^(x)f(t)dt and if int(f'(x)+F(x))cos xdx=2 ,then the value of f(0) is

Let f:[0,oo)->R be a continuous strictly increasing function, such that f^3(x)=int_0^x t*f^2(t)dt for every xgeq0. Then value of f(6) is_______