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)`

Check the function f defined by f(x) = (x+2) e^(−x) is (a)decreasing for all x (b)decreasing in (−∞,−1) and increasing in (−1,∞) (c)increasing for all x (d) increasing in (−∞,−1) and decreasing in (−1,∞).

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)

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 f defined by f(x)=x^2−x+1 is neither increasing nor decreasing in (−1,1) . Hence find the intervals in which f(x) is strictly increasing and strictly decreasing.

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

The function f(x)=x^2-x+1 is increasing and decreasing in the intervals

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]

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

The function f(x)=x/(1+|x|) is (a) strictly increasing (b) strictly decreasing (c) neither increasing nor decreasing (d) none of these

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .