Let `f` be continuous and differentiable function such that `f(x)` and `f'(x)` has opposite signs everywhere. Then (A) `f` is increasing (B) `f` is decreasing (C) `|f|` is non-monotonic (D) `|f|` is decreasing

Let a continous and differentiable function f(x) is such that f(x) and (d)/(dx)f(x) have opposite signs everywhere. Then,

Let f:R rarr R be a differentiable function for all values of x and has the property that f(x) andf '(x) has opposite signs for all value of x. Then,(a) f(x) is an increasing function (b) f(x) is an decreasing function (c)f^(2)(x) is an decreasing function (d)|f(x)| is an increasing function

Let f(x) be continuous and differentiable function everywhere satisfying f(x+y)=f(x)+2y^(2)+kxy and f(1)=2, f(2)=8 then the value of f(3) equals

Let f(x) be a continuous function such that f(0)=1 and f(x)=f((x)/(7))=(x)/(7)AA x in R then f(42) is

A continuous and differentiable function f(x) is increasing in (-oo,3/2) and decreasing in (3/2,oo) then x=3/2 is

Let f(x) be a non-constant twice differentiable function defined on (oo,oo) such that f(x)=f(1-x) and f'(1/4)=0^(@). Then

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

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)

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)