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]`

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]

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]

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]

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): [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)= 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)

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