If `f(x)=xe^(x(1-x))` , 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.e^(x(1-x)) , then f(x) is

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

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(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

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

If f' (x) =xe^(x) and f(0)=1, find f(x)

If fogoh(x) is an increasing function, then which of the following is not possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n dg(x) are decreasing and h(x) is increasing (c) f(x),g(x),a n dh(x) are decreasing

If f(x)= int e^(x)(x-1)(x-2)dx , then show that f(x) is a decreasing function 1 lt x lt 2 .

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.