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,∞).

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)

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)= 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)

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

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]

Prove that the function f(x)=(2x-1)/(3x+4) is increasing for all x R.

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

Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasing.

Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasing.