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

Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi//2,\ pi) and neither increasing nor decreasing in (0,\ pi) .

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)

Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-pi,0) and neither increasing nor decreasing in (-pi,pi)dot

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

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

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)

Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasing.