Let `f: R->R` be a twice differentiable function such that `f(x+pi)=f(x)` and `f^(x)+f(x)geq0` for all `x in Rdot` Show that `f(x)geq0` for all `x in Rdot`

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to

Let f:(0,oo)rarr 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 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 be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

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

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

if f:R rarr R is a differentiable function such that f'(x)>2f(x) for all x varepsilon R, and f(0)=1, then

Let f be a polynomial function such that f(3x)=f'(x);f''(x), for all x in R. Then : .Then :

Let F:R-R be a thrice differentiable function.Suppos that F(1)=0,F(3)=-4 and F(x)<0 for all x in((1)/(2),3)* Let f(x)=xF(x) for all x in R The correct statement is