It is proved that if the function f (x) is a strictly increasing function on [a, b], then the equation f (x) = 0 has at most one real root on the interval [a, b]

Suppose that the equation f (x) = 0 has at least two real roots x1, X2 ∈ [a, b]
So f (x1) = f (x2) = 0
According to Rolle's theorem, there must be a point C ∈ (x1, x2) such that f '(c) = 0 holds
Strictly increasing contradiction with F (x)!
So there is only one real root at most!

It is proved that if the function f (x) is a strictly increasing function on [a, b], then the equation f (x) = 0 has at most one real root on the interval [a, b]

It is proved that if the function f (x) is a strictly increasing function on [a, b], then the equation f (x) = 0 has at most one real root on the interval [a, b]

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