1. Assume y is continuous on [c, d] and differentiable on (c,d). (a) Ify is non-decreasing (monotone increasing) is it true that ≥0? (Either prove your answer or give a counterexample). (b) If y is strictly increasing, is it true that y'>0? Either give a counterexample and show where the proof of (a) fails or prove your statement.

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Chapter2: Second-order Linear Odes
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1. Assume is continuous on [c, d] and differentiable on (c,d).
(a) If ✅ is non-decreasing (monotone increasing) is it true that ✅′ ≥ 0? (Either
prove your answer or give a counterexample).
(b) Ify is strictly increasing, is it true that y > 0? Either give a counterexample
and show where the proof of (a) fails or prove your statement.
Transcribed Image Text:1. Assume is continuous on [c, d] and differentiable on (c,d). (a) If ✅ is non-decreasing (monotone increasing) is it true that ✅′ ≥ 0? (Either prove your answer or give a counterexample). (b) Ify is strictly increasing, is it true that y > 0? Either give a counterexample and show where the proof of (a) fails or prove your statement.
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