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If f(x) is continuous for a ≤ x ≤ b and differentiable for a < x < b, then there is some value of x between a and b, say c, for which:

df dx (c) = f(b)−f(a) b−a

i.e. there is a point where the tangent to f(x) is parallel to the straight line joining (a,f(a)) and (b,f(b)).