f : [a, b] → R is continuous and in the open interval (a,b) differentiable. f...

f : [a, b] → R is continuous and in the open interval (a,b) differentiable. f rises strictly monotonously ⇒ ∀x ∈ (a, b) : f ′(x) > 0. (TRUE or FALSE?) f rises strictly monotonously ⇐ ∀x ∈ (a, b) : f ′(x) > 0. (TRUE or FALSE?) f is constant ⇐⇒ ∀x∈(a,b): f′(x)=0 (TRUE or FALSE?) If f is reversable, f has no critical point. (TRUE or FALSE?) If a is a “minimizer” of f, then f ′(a) = 0. (TRUE or FALSE?) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0. If f is reversable, then f −1 differentiable. (TRUE or FALSE?) If f ′ is limited, then f is lipschitz. (TRUE or FALSE?)

Expert Solution

Here, mainly we use Mean value theorem to justify the statements.

Colby Messinger answered 3 years ago

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Question

f : [a, b] → R is continuous and in the open interval (a,b) differentiable. f...

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Expert Solution

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