6) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., 0) for all E (a, b). Prove that there exists c E (a, b) such thatn ) =è¨ã·(Hint consider the function fu)-..-. 0.1f there exists a function,(z)such that hat 71eHint consider the function 7le-, there exists a function g (x) such that f (c)1 f(c) a-cb-c f(z) ab-ja g, (z) = fr) _ a12-b1 such c E (a, b)) ,theng, (c) = 0 yields f(c) =ã¼+b1 Now find suchg(z) and use MVT to show the existence of f(c) a-cb-c
Show transcribed image text 6) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., 0) for all E (a, b). Prove that there exists c E (a, b) such thatn ) =è¨ã·(Hint consider the function fu)-..-. 0.1f there exists a function,(z)such that hat 71eHint consider the function 7le-, there exists a function g (x) such that f (c)1 f(c) a-cb-c f(z) ab-ja g, (z) = fr) _ a12-b1 such c E (a, b)) ,theng, (c) = 0 yields f(c) =ã¼+b1 Now find suchg(z) and use MVT to show the existence of f(c) a-cb-c