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)`

f(x) is a strictly increasing function, if f'(x) is :

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)

The function f(x)=ax+b is strictly increasing for all real x is

The function f(x) = ax + b is strictly increasing for all real x if

If f(x)=x^3+b x^2+c x+d and 0 le b^2 le c , then a) f(x) is a strictly increasing function b)f(x) has local maxima c) f(x) is a strictly decreasing function d) f(x) is bounded

If f(x)=x^3+b x^2+c x+d and 0

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) .

if a function f(x) is (i) continuous on [a,b] (ii) derivable on (a,b) and (iii) f(x) gt 0 x in (a,b) then show that f(x) is strictly increasing on [a,b]

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)