`f: RvecR ,f(x)` is differentiable such that `f(f(x))=k(x^5+x),k!=0)dot` Then `f(x)` is always increasing (b) decreasing either increasing or decreasing non-monotonic

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

If f(x)=x^(3/2)(3x-10),xgeq0, then f(x) is increasing in ____.

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

f(x)=(x)/(1+|x|) then f is differentiable at

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is a. increasing in (0,3a) decreasing in (3a, 4a) b. increasing in (a, 4a) decreasing in (5a ,oo) c. increasing in (0,4a) d. none of these

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

The function f(x) = x^(2) is decreasing in

H(x) increase as f(x) decreases for all real values of x if