Question

Question 11 Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? x f(x)= on the interval [1,10]. If it satisfies the hypotheses, X +5 find all numbers c that satisfy the conclusion of the Mean Value Theorem.

I need answers 11, 12, 13, 14, 15

Answer 1

Soo- Given f(") * () - X. 대0) 45 것 c); })-do) bra Hede : 10 ite: to: 6 TD +) { Co) 23 10+ (+5) 1 - =일«J CMJ dn (+5) 5 e) 이스s (Ct52 (A+S) - C ماده 5 (C+5) 2 10-1 - 5 (Ct52 1 18 ~ 4.486 lies in (1,10] = -5490 there bose mean value theorm satistes 1 10) co Given 6 () = vx - (8) (81) - V51 - (해) 공 (0) - - - 0 $60736(81) function is continous edittern those in (0,81] '): 늙 fc10 글 - ㅗ ft) ) 21c 1 2C 8] q 81 니 lies in [0,81] Hence Rolle's theoom is satibed C- 다.

Given tor= x²6x + 2 t'in = 2n-6 I'(x ) = 0 23-620 2x = 6 2- 3 At 21 f(). 1-6X1 + 2 C-3 =-7 Ata=3, $(3): 9-18 + 2 Atx=4 , $(4):16–24+2 = -6 Global minimum Global minimum value is -7 value is a7 at n=3 Global maximum value is -3 at aal do Given 27 37712 2 3+02 du put us =an on s du > encuite undo substitution en ( 370²) to