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songoku

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- What is the condition required (related to first derivative) for a function to be increasing function and monotonic increasing function?

I will start from the meaning of increasing function. A function is said to be increasing function if for x < y then f(x) ≤ f(y). Is this correct?

Then f(x) is increasing function if f'(x) ≥ 0. Is this correct?

Lately I encounter the term "monotonic increasing". What is the difference between monotonic increasing and increasing? Is monotonic increasing function the one where if x < y then f(x) < f(y)?

Then f(x) is monotonic increasing function if f'(x) > 0?

Then f(x) is increasing function if f'(x) ≥ 0. Is this correct?

Lately I encounter the term "monotonic increasing". What is the difference between monotonic increasing and increasing? Is monotonic increasing function the one where if x < y then f(x) < f(y)?

Then f(x) is monotonic increasing function if f'(x) > 0?