Define the strictly increasing function and strictly decreasing function on an interval.

Strictly increasing functions and strictly decreasing functions

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).

In case of strictly decreasing function, the derivative is

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

Let f and g be two differentiable functions defined on an interval I such that f(x)>=0 and g(x)<= 0 for all x in I and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

Let f and g be two differentiable functions defined on an interval I such that f(x)>=0 and g(x)<= 0 for all x in I and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

A function f is said to be increasing/strictly increasing/decreasing/strictly decreasing at x_0, if there exists an interval I containing x_0, such that f is increasing /strictly increasing /decreasing /strictly decreasing, respectively, in I. Which of the following statements regarding the above definition is FALSE?

The function f(x) = x^(2) - 2 x is strictly decreasing in the interval