Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f...

Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f is non-decreasing on [a,b] if and only if f′(x) ≥ 0 for all x ∈ (a,b), while if f is non-increasing on [a,b] if and only if f′(x) ≤ 0 for all x ∈ (a, b).

can you please prove this theorem? thank you!

Expert Solution

Colby Messinger answered 2 years ago

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Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f...

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