AP Calc BC Unit 1.3 - Differentiability

When we zoom in on a differentiable point…

it looks like a line (“locally linear”)

differentiable

a function that is always locally linear

differentiability theorem

1. If a function is differentiable, then it is continuous. Differentiability implies continuity

2. If f is differentiable at x=c, then f is continuous at x=c

If f is differentiable, then it is continuous

true

If not differentiable, then not continuous

false

if continuous, then differentiable

false

if not continuous, then not differentiable

true