Question

graph a function increasing at (-infinity,-2), decreasing at (2,infinity), and constant at (-2,2)

Answer 1

Ahhhh! it's cookie mostah! :D man that looks delicious +_+

Answer 2

yeah. I know

Answer 3

Increasing over \((-\infty,-2)\) means \(f'(x)>0\) for \(x<-2\).

Similarly, decreasing over \((2,\infty)\) means \(f'(x)<0\) for \(x>2\).

Constant over \((-2,2)\) means \(f'(x)=0\) for all \(x\in(-2,2)\).

Judging by this information, \(f(x)\) can be easily modeled by a piecewise function. Try to see if you can fill in the blanks:
\[f(x)=\begin{cases}g(x)&\text{for }x<2\\h(x)&\text{for }-2<x<2\\k(x)&\text{for }x>2\end{cases}\]
It doesn't matter what \(f(x)\) is assigned to for \(x=\pm2\) in this case, since it's not required that \(f\) be continuous at these points; only that its components are differentiable.

Clearly \(h(x)\) is some constant function, so you can choose any number here. Find some \(g,k\) that work.

Answer 4

OMG!!! thank you so much. It makes sense now!!!

Answer 5

You're welcome!