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

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

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

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

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

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

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)

Prove that f(x)=a x+b , where a , b are constants and a >0 is an increasing function on Rdot