Local Linearity.

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Presentation transcript:

Local Linearity

A nice graph Consider a small portion of the graph . . .

“Zooming In” Consider a small portion of the graph . . . . . . . shown here in blue.

Zooming Now “zoom in” on the blue part of the graph. . .

“Zooming In” And repeat the process by zooming in on the part colored in pink. . .

“Zooming In” Keep it up. . .

“Zooming In”

“Zooming In”

“Zooming In”

Typical Behavior

In general. . . When we zoom in on a “sufficiently nice” function, we see a straight line.

Local Linearity

Differentiability