a) Suppose f:[a, b] → R is continuous on [a, b] and differentiable on (a, b)...

a) Suppose f:[a, b] → R is continuous on [a, b] and differentiable on (a, b) and f ' < -1 on (a, b). Prove that f is strictly decreasing on [a, b].
b) Suppose f:[a, b] → R is continuous on [a, b] and differentiable on (a, b) and
f ' ≠ -1 on (a, b). Why must it be true that either f ' > -1 on all of (a, b) or f ' < -1 on all of (a, b)?

Expert Solution

Colby Messinger answered 2 years ago

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Question

a) Suppose f:[a, b] → R is continuous on [a, b] and differentiable on (a, b)...

Solutions

Expert Solution

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