Prove that `f(x) = x^(2) -x + 1` is neither encreasing nor decreasing in [0,1]

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

f'(x) = x^(2) - 5x + 4 then f(x) is decreasing in

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

Show that the function given by f (x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

For each of the following graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a. (##CEN_GRA_C01_S01_018_Q01.png" width="80%">

Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot Hence, prove that (2x)/pi

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)=x^3-3(a-2)x^2+3ax+7 and f(x) is increasing in (0,1] and decreasing is [1,5) , then roots of the equation (f(x)-14)/((x-1)^2)=0 is (A) 1 (B) 3 (C) 7 (D) -2

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)

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).