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]

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)

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)

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): [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)

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

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.

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing

Find the intervals of increasing and decreasing function for f(x)=x^(3)+2x^(2)-1 .