The function defined by f(x)=(x+2)e^(-x)...

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

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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)

Prove that the function f(x)=x+1/x (x ne 0) is decreasing for all x in (-1, 0) uu (0, 1) .

Prove that the function f(x) = x+1/x(x!=0) is decreasing for all x in (-1,0)uu(0,1) .

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

(i) The function f(x)=x^(3) is decreasing in (-oo, oo) (ii) The function f(x)=x^(4) is increasing in (-oo, 0) , then-

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]

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 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)

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)

Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing for every x in (-oo,1)uu(2,3) Statement 2: f(x) is increasing for x in (1,2)uu(3,oo) and has no point of inflection.

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