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(x) = xsqrt(4ax-x^(2)),(agt0) Then f(x) is

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,pi/e), decreasing in (pi/e ,oo) decreasing in (0,pi/e), increasing in (pi/e ,oo)

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]

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

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

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

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)

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

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)