Let f be a differentiable real function defined on `(a; b)` and if `f'(x) > 0` for all ` x in (a; b)` then f is increasing on `(a; b)` and if `f'(x) < 0` for all ` x in (a; b)` then `f(x)` is decreasing on `(a; b)`

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

Let f be a function defined on [a,b] such that f'(x)>0 for all quad x in(a,b) ( Then prove that f is an increasing function on (a,b).

Let f be continuous on [a;b] and differentiable on (a;b) If f(x) is strictly increasing on (a;b) then f'(x)>0 for all x in(a;b) and if f(x) is strictly decreasing on (a;b) then f'(x)<0 for all x in(a;b)

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 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:

Given that f is a real valued differentiable function such that f(x) f'(x) lt 0 for all real x, it follows that

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f:R rarr R be a function defined by f(x)=|x] for all x in R and let A=[0,1) then f^(-1)(A) equals