Question

How do you know what is the rate of change of the steepest section of an absolute value graph?

Answer 1

This is my function, so would I use 251 and find the rate of change?

Answer 2

The rate of change as the steepest part? Well the derivative is undefined for one.

Answer 3

You mean the tip, right?

Answer 4

Why is it undefined? What do you mean by the tip though?

Answer 5

What do you mean by the steepest part? The curve is uniformly steep everywhere except at the tip.

Answer 6

The tip is where it changes directions.

Answer 7

Oh I see what you mean! Yeah, I meant at the tip, my bad for not stating that

Answer 8

So this means it'll be undefined?

Answer 9

Yeah. If you look at the slope, it jumps between 1 and -1 at the tip.

Answer 10

This jump is done at a single point, not over an interval. Thus we know the slope is not continuous.

Answer 11

Here is the graph of the function to get a better idea: