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]`

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)

Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0

f:R rarr R,f(x) is differentiable such that f(f(x))=k(x^(5)+x),k!=0). Then f(x) is always increasing (b) decreasing either increasing or decreasing non-monotonic

Let varphi(x)=f(x)+f(2a-x) and f"(x)>0 for all x in [0, a] . Then, varphi(x) (a) increases on [0, a] (b) decreases on [0, a] (c) increases on [-a , 0] (d) decreases on [a , 2a]

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

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)

f(x) = (1-x)^(2) cdot sin^(2) x + x^(2) ge 0, AA x and g(x) =int_(1)^(x) ((2(t-1))/((x+1))-log t ) f (t) dt Which of the following is true? (A)g is increasing on (1,infty) (B)g is decreasing on (1, infty) (C) g is increasing on (1,2) and decreasing on (2, infty) (D) g is decreasing on (1,2) and increasing on (2,infty)

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then fis (A) increasing in (0,pi) and decreasing in (-oo,0)(B) increasing in (-oo,0) and decreasing in (0,oo)(C) increasing in (-oo,oo) and (D) decreasing in (-oo,oo)

Show that f(x)=(1)/(1+x^(2)) is neither increasing nor decreasing on R.

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)