let-f-a-b-R-continue-let-suppose-f-derivable-on-a-b-and-x-a-b-f-x-gt-0-prove-that-c-a-b-f-b-f-a-e-b-a-f-c-f-c- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 30212 by abdo imad last updated on 18/Feb/18 letf[a,b]→Rcontinueletsupposefderivableon[a,b]and∀x∈[a,b]f(x)>0provethat∃c∈]a,b[/f(b)f(a)=e(b−a)f,(c)f(c). Commented by abdo imad last updated on 21/Feb/18 duetof(x)>0letputφ(x)=ln(f(x))φiscontinueon[a,b]T.A.F⇒∃c∈]a,b[/φ(b)−φ(a)=(b−a)φ′(c)⇒ln(f(b))−ln(f(a))=(b−a)f′(c)f(c)⇒ln(f(b)f(a))=(b−a)f′(c)f(c)⇒∃c∈]a,b[/f(b)f(a)=e(b−a)f′(c)f(c). Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-161281Next Next post: y-sin-x-cos-x- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.