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 f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

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

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot 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 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 be a function which is continuous and differentiable for all real x. If f(2)=-4 and f'(x) >= 6 for all x in [2,4], then

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx)

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f be a continuous real function such that f(11)=10 and for all x ,f(x)f(f(x))=1 then f(9)= 9 (b) 1/9 (c) (10)/9 (d) 9/(10)