Assignment 5: Smooth function

Assignment 5: Smooth function

A smooth function is a function that has continuous derivatives up to some desired order over some domain.

y=-2|x-1|+3
We can separate this function to three parts:
y=-2(x-1)+3=-2x+5  when x>1
y=-2(1-1)+3=3         when x=1
y=2(x-1)+3=2x+1     when x<1

We can see from the first graph, the max of this function is 3.

But when x<1 , the function have a positive slope.

when x>1, the function have a negative slope.

when x=1, the function's slope is exist.

Because the when X=1, the slope is not exit, so this function is a non-smooth function.