Questions about the Mean Value Theorem and monotonic functions

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Question: mean value theorem
Select the true statements involving the mean value theorem and monotonicity.a) If 𝑓′(𝑥)‹0 for all 𝑥 in an interval, then 𝑓 is increasing on that interval.b) If 𝑓 is continuous on [𝑎,𝑏] and differentiable on (𝑎,𝑏), then there exists at least one 𝑐 in (𝑎,𝑏) such that 𝑓(𝑏)−𝑓(𝑎)=𝑓′(𝑐)(𝑏−𝑎).c) If 𝑓 is continuous on [𝑎,𝑏], then there exists at least one 𝑐 in (𝑎,𝑏) such that 𝑓′(𝑐)=𝑓(𝑏)−𝑓(𝑎)/𝑏−𝑎.d )If 𝑓 is differentiable and 𝑓′(𝑥)=0 for all 𝑥∈(𝑎,𝑏), then 𝑓 is constant on [𝑎,𝑏].e) If 𝑓′(𝑥)›0 for all 𝑥 in an interval, then 𝑓 is decreasing on that interval

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Sam C.
Math and Physics Tutor with over 7 years experience
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