The real function `f(x)=2x^3-3x^2-36x+7` is:
a) Strictly increasing in `(-oo,-2)` and strictly decreasing in `(-2,oo)`
b) strictly decreasing in `(-2,3)`
c) Strictly decreasing in `(-oo,3)` and strictly increasing in `(3,oo)`
d) strictly decreasing in `(-oo,-2)uu(3,oo)`

Strictly increasing functions and strictly decreasing functions

The function f(x)=4x^(3)-6x^(2)-72x+30 is strictly decreasing on interval.

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Show that the function f(x) = x^(2) is (a) strictly increasing on [0, oo] (b) strictly decreasing on [-oo, 0] (c) neither strictly increasing nor strictly decreasing on R

Show that the function f(x)=x^(2) is a strictly decreasing function on (-oo,0].

show that the function f(x)=sin x is strictly increasing in (0,(pi)/(2)) strictly decreasing in ((pi)/(2),pi)

Find the interval in which f(x)=x^(3)-3x^(2)-9x+20 is strictly increasing or strictly decreasing.

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

Show that the function f(x ) = |x| is (a) striclty increasing on [0, oo] (b) strictly decreasing on [-oo, 0]