If `f:[0,1] to [0,prop)` is differentiable function with decreasing first derivative suc that f(0)=0 and `f'(x) gt 0`, then

If f:[0,1] to [0,oo) is differentiable function with decreasing first derivative such that f(0)=0 and f'(x) gt 0 , then

Let f:[0,1]rarr[0,oo) be a differentiable with decreasing first derivative &f(0)=0 ,then int_(0)^(1)(dx)/(f^(2)(x)+1) is (A) <(tan^(-1)f(1))/(f'(1)) (B) <(f(1))/(f'(1)) (C) <(tan^(-1)f'(1))/(f'(1)) (D) <=(f(1))/(f'(1))

Let f(x) have second derivative at c such that f'(c )=0 and f''(c ) gt 0 , then c is a point of :

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then lim_(x->0)(f(x)-1)/x is a. 1//2 b. 1 c. 2 d. 0

Let f:R rarr 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

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then