" For all twice differentiable functions "f:R rarr R," with "f(0)=f(1)=f(0)=0

For all twice differentiable functions f : R to R , with f(0) = f(1) = f'(0) = 0

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

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 such that f(0)=f(1)=f(2)=0 . 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 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: \mathbb{R} rarr \mathbb{R} be a twice differentiable function such that f(x+pi)=f(x) and f''(x) + f(x) geq 0 for all x in \mathbb{R} . Show that f(x) geq 0 for all x in \mathbb{R} .

Let f: \mathbb{R} rarr \mathbb{R} be a twice differentiable function such that f(x+pi)=f(x) and f''(x) + f(x) geq 0 for all x in \mathbb{R} . Show that f(x) geq 0 for all x in \mathbb{R} .