So anyway, the derivative of abs(x+2) is (x+2)/(abs(x+2))... I know how to do the work.. Question is when they ask is is strictly monotonic on [-2, \inf) ____[----). Its a straight line, so would it be?

Question

So anyway, the derivative of abs(x+2) is (x+2)/(abs(x+2))... I know how to do the work.. Question is when they ask is is strictly monotonic on [-2, \inf) ____[----).  Its a straight line, so would it be?

anonymous · Answer

Not all straight lines are strictly monotonic (though this may vary depending on your definition of "monotonic"). For example, the line $y=0$ would not be considered strictly monotonic (strictly speaking) because strict monotonicity requires that, for $x_1<x_2$, you have $y(x_1)>y(x_2)$ or $y(x_1)<y(x_2)$ for strictly increasing and decreasing functions, respectively.