We’re starting a new unit: applications of diﬀerentiation.

We’re going to do two applicationstoday. The ﬁrstislinear approximations,

which are encompassed by the single formula:

f(x) ≈ f(x0)+f'(x0)(x−x0),

but it will take at least half an hour to explain how this formula is used.

The teacher explains that the right hand side is the equation for the tangent line? Or am I misunderstanding?

If I am not, how come this is the equation for the tangent line? I thought there was only one definition for that.