Question

TOPIC: intermediate value theorem
show that the equation x^3-2x+3x-1=0 has a solution in the interval [0,1]

Answer 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: