30 июн. 2017 г. · Since derivatives have the intermediate value property (theorem 5.12), it follows that derivatives cannot have simple discontinuities.

26 авг. 2019 г. · Let x′7∈(a,x′6). Then, g(x′4)<g(x′4)2<g(x′7). Then, by the intermediate value theorem, g(x′8)=g(x′4)2 for some x′8∈(x′7,x′4).

17 мар. 2019 г. · I'm having trouble understanding the proof for the intermediate value theorem for derivatives. Here is the thereom from Rudin: Suppose f is a ...

30 янв. 2021 г. · Real function with intermediate value property and one more property as set {x:f(x)=r} is always closed for every rational r, is continuous.

27 авг. 2020 г. · A single variable real function is continuous when it has a derivative, so we can apply the Mean Value Theorem to the sums used in the proof.

11 мая 2015 г. · Yep, this looks correct. Perhaps you should stress the fact that supE is adherent to [a,b]∖E because f(b)>0.

4 февр. 2017 г. · Theorem 7.17 in Baby Rudin: How is a shorter proof possible if the continuity of the f′n is assumed in addition?

11 июл. 2023 г. · If there exists C(x)<0 for some x>0, by the intermediate value theorem, there exists a x>0, C(x)=0 contradicts to the assumption. Share.

23 сент. 2021 г. · Since C(π2)=0⩽x⩽1=C(0) and C is continuous, it follows from the intermediate value theorem that there is some t∈[0,π2] such that C(t)=x.

1 нояб. 2015 г. · Each "break point" yi=α(a)+iΔα is a value of α by continuity (the intermediate value property), so there exists an xi in [a,b] such that yi=α(xi) ...