If we...

take a continuous and smooth function and zoom in close enough, than it looks like a line

Lines are...

important because they have slope!

Using

LL (Local Linearity) we can find the slope of a curve using a single point using LL lots of times we can find a pattern/equation for the slope

This...

patern recognition for the slope is called the derivative

The...

derivative lets us find the slope of an entire curve at the same time

What is Intermediate Value Theorem

The Intermediate Value Theorem (IVT) is a fundamental concept in calculus stating that if a continuous function \(f\) covers an interval from \(a\) to \(b\), it must take on every value between \(f(a)\) and \(f(b)\). Because the function is continuous, its graph has no breaks or gaps, forcing it to cross any intermediate horizontal line