Let `f: RvecR` be a differentiable function for all values of `x` and has the property that `f(x)a n df^(prime)(x)` has opposite signs for all value of `xdot` Then, `f(x)` is an increasing function `f(x)` is an decreasing function `f^2(x)` is an decreasing function `|f(x)|` is an increasing function

Options

A. f(x) is an iincreasing function
B. f(x) is a decreasing function
C. `f^(2)(x)` is a decreasing function
D. |f(x)| is an increasing function

Answer

3

Explanation

f(x) `f'(x) lt 0 forall x in R`
or `1/2 (d)/(dx)(f^(2))(x)lt0`
or `(d)/(dx)(f^(2))(x)lt0`
Thus `f^(2)` (x) decreasing function