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krypton
TOPIC: intermediate value theorem show that the equation x^3-2x+3x-1=0 has a solution in the interval [0,1]
In essence the theorem states that given any function f continuous on the interval [a, b] and differentiable on the open (a, b) interval then there at least some point c in the interval (a, b) such that the tangent to the curve c is parallel to the straight secant connecting the points (a, f (a)) and (b, f (b)). That is to say: