Let `f` be continuous and differentiable function such that `f(x)` and `f'(x)` has opposite signs everywhere. Then (A) `f` is increasing (B) `f` is decreasing (C) `|f|` is non-monotonic (D) `|f|` is decreasing

Let f:Rto R be a twice continuously differentiable function such that f(0)=f(1)=f'(0)=0 . Then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

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 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

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x) = xf'(x). Then

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x)=xf'(x) . Then-

Let f be any continuously differentiable function on [a,b] and twice differentiable on (a,b) such that f(a)=f'(a)=0 . Then

Let f be a twice differentiable function such that f"(x) = -f(x) , and f'(x) = g(x) , h(x)=[f(x)]^2+[g(x)]^2 Find h(10), if h(5) = 11