NOTE- If it is true, you need to prove it and If it is false, give...

NOTE- If it is true, you need to prove it and If it is false, give a counterexample

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

a) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0. (TRUE or FALSE?)

b) If f is reversable, then f −1 differentiable. (TRUE or FALSE?)

c) f is constant ⇐⇒ ∀x∈(a,b): f′(x)=0 (TRUE or FALSE?)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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