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# Derivatives

# Tangent Line Approximation

There are only two things we need to remember about the tangent line to *f* at *a*.

**The tangent line and***f*have the same*y*-value at*a*.

That is, the point (*a*,*f*(*a*)) is on*f*and also on the tangent line to*f*at*a*.

**The tangent line and***f*have the same slope at*a*.

That is, the slope of the tangent line to*f*at*a*is*f'*(*a*).