The theorem that guarantees a root of a continuous f on [a, b] when f(a)·f(b) < 0 is the:
Review of Calculus
Continuity, the Intermediate and Mean Value Theorems, and Taylor polynomials with their remainder.
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All polynomials are functions but not all functions are polynomials.
Notes
Intermediate Value Theorem: f continuous on [a, b] and K between f(a) and f(b) ⇒ some c in (a, b) has f(c) = K. It is why bisection works.
Taylor: f(x) = Pₙ(x) + Rₙ(x), Rₙ(x) = f⁽ⁿ⁺¹⁾(ξ)(x − x₀)ⁿ⁺¹/(n + 1)!
Exam angle
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