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Define Newton’s difference quotient
a function f is differentiable at x iff
Properties of derivatives
If f : [a,b] → R is continuous and f : (a,b) → R is differentiable, then there exists c ∈ (a,b) such that…
If f is n times differentiable in (a, b) with x0 ∈ (a, b), then for any x ∈ (a, b) we have:
Lagrange error term
L’Hopital’s rule